Five cards are drawn randomly from a standard deck of 52 cards.
Determine the probability that exactly 3 of these cards are Aces. Write your answer in decimal form, rounded to 5 decimal
places
Answer:
Answers
=========================================================
Explanation:
There are 4 ways to select 3 aces where order doesn't matter. It's basically the same as saying there are 4 ways to leave out one ace.
Then we have 2 slots left to fill. There are (48*47)/2 = 1128 ways to do this where order doesn't matter. The 48 is from the fact there are 52-4 = 48 cards that aren't aces. We step down to 47 after picking the first non-ace card. The 2 in the denominator is to correct for double counting.
We found there were 4 ways to pick the three aces, and 1128 ways to pick the other two non-ace cards. Overall, there are 4*1128 = 4512 ways to pick all five cards where we have exactly 3 aces.
This is out of 52C5 = 2,598,960 ways to select any five cards from a 52 card deck. I'm using the nCr formula which is
[tex]_n C _r = \frac{n!}{r!*(n-r)!}[/tex]
Use n = 52 and r = 5 to get the value mentioned. The exclamation marks indicate factorial.
------------------------------------
To recap, there are
4512 ways to pick exactly three aces2,598,960 ways to pick five cards without any restrictionsDividing the two values gets us the final answer
4512/(2,598,960) = 0.001736079047
This value rounds to 0.00174
The probability that exactly 3 of these cards are Aces is 0.004%.
Given that five cards are drawn randomly from a standard deck of 52 cards, to determine the probability that exactly 3 of these cards are Aces the following calculation must be performed:
Each particular probability must be multiplied by each other, and its result by one hundred, to obtain the probability percentage. (3/52 x 2/51 x 1/50) x 100 = X 0.004 = X
Therefore, the probability that exactly 3 of these cards are Aces is 0.004%.
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Related Questions
Determine whether the series is convergent or divergent by expressing sn as a telescoping sum.
[infinity]
Σ 8/n^2-1
n=3
Answers
Answer:
The sum converges at: [tex]\frac{10}{3}[/tex]
Step-by-step explanation:
Given
[tex]\sum\limits^{\infty}_{n =2} \frac{8}{n^2 - 1}[/tex]
Express the denominator as difference of two squares
[tex]\sum\limits^{\infty}_{n =2} \frac{8}{(n - 1)(n+1)}[/tex]
Express 8 as 4 * 2
[tex]\sum\limits^{\infty}_{n =2} \frac{4 * 2}{(n - 1)(n+1)}[/tex]
Rewrite as:
[tex]4 * \sum\limits^{\infty}_{n =2} \frac{2}{(n - 1)(n+1)}[/tex]
Express 2 as 1 + 1 + 0
[tex]4 * \sum\limits^{\infty}_{n =2} \frac{1+1+0}{(n - 1)(n+1)}[/tex]
Express 0 as n - n
[tex]4 * \sum\limits^{\infty}_{n =2} \frac{1+1+n - n}{(n - 1)(n+1)}[/tex]
Rewrite as:
[tex]4 * \sum\limits^{\infty}_{n =2} \frac{(n + 1)-(n - 1)}{(n - 1)(n+1)}[/tex]
Split
[tex]4 * \sum\limits^{\infty}_{n =2} \frac{(n + 1)}{(n - 1)(n+1)}-\frac{(n - 1)}{(n - 1)(n+1)}[/tex]
Cancel out like terms
[tex]4 * \sum\limits^{\infty}_{n =2} \frac{1}{(n - 1)}-\frac{1}{(n+1)}[/tex]
In the above statement, we have:
[tex]a_3 + a_5 = 4[(\frac{1}{2} - \frac{1}{4}) + (\frac{1}{4} - \frac{1}{6})][/tex]
[tex]a_3 + a_5 = 4[(\frac{1}{2} - \frac{1}{6})][/tex]
Add [tex]a_7[/tex]
[tex]a_3 + a_5 + a_7= 4[(\frac{1}{2} - \frac{1}{6}) + (\frac{1}{7 - 1} - \frac{1}{7+1})][/tex]
[tex]a_3 + a_5 + a_7= 4[(\frac{1}{2} - \frac{1}{6}) + (\frac{1}{6} - \frac{1}{8})][/tex]
[tex]a_3 + a_5 + a_7= 4[(\frac{1}{2} - \frac{1}{8})][/tex]
Notice that the pattern follows:
[tex]a_3 + a_5 + a_7 + ...... + a_{k}= 4[(\frac{1}{2} - \frac{1}{k+1})][/tex]
The above represent the odd sums (say S1)
For the even sums, we have:
[tex]4 * \sum\limits^{\infty}_{n =2} \frac{1}{(n - 1)}-\frac{1}{(n+1)}[/tex]
In the above statement, we have:
[tex]a_4 + a_6 = 4[(\frac{1}{3} - \frac{1}{5}) + (\frac{1}{5} - \frac{1}{7})][/tex]
[tex]a_4 + a_6 = 4[(\frac{1}{3} - \frac{1}{7})][/tex]
Add [tex]a_8[/tex] to both sides
[tex]a_4 + a_6 +a_8 = 4[(\frac{1}{3} - \frac{1}{7}) + \frac{1}{7} - \frac{1}{9}][/tex]
[tex]a_4 + a_6 +a_8 = 4[\frac{1}{3} - \frac{1}{9}][/tex]
Notice that the pattern follows:
[tex]a_4 + a_6 + a_8 + ...... + a_{k}= 4[(\frac{1}{3} - \frac{1}{k+1})][/tex]
The above represent the even sums (say S2)
The total sum (S) is:
[tex]S = S_1 + S_2[/tex]
[tex]S =4[(\frac{1}{2} - \frac{1}{k+1})] + 4[(\frac{1}{3} - \frac{1}{k+1})][/tex]
Remove all k terms
[tex]S =4[(\frac{1}{2}] + 4[(\frac{1}{3}][/tex]
Open bracket
[tex]S =\frac{4}{2} + \frac{4}{3}[/tex]
[tex]S =\frac{12 + 8}{6}[/tex]
[tex]S =\frac{20}{6}[/tex]
[tex]S =\frac{10}{3}[/tex]
The sum converges at: [tex]\frac{10}{3}[/tex]
!!!!!!!1I WILL GIFT YOU MANY POINTSSSSS
Answers
Answer:
The third one down
Step-by-step explanation:
m, Slope is negative
b, Y-intercept is positive
help answer please help
Answers
Answer:
The best was to display a set of data with a wide range would be
a histogram.
Step-by-step explanation:
It's a graphical display of bars which will help you measure the central tendency.
A bag holds 20 red marbles and 40 green ones, for a total of 60 marbles. Ryan picks one marble from the bag at random, hoping to pick a red marble. Which of the following statements is true?
a. The probability that Ryan will pick a red marble on the first try is 67%. If he keeps this marble and picks another from the bag, the probability that he will pick a green marble decreases.
b. The probability that Ryan will pick a red marble on the first try is 33%. If he keeps this marble and picks another from the bag, the probability that he will pick a green marble increases.
c. The probability that Ryan will pick a red marble on the first try is 33%. If he keeps this marble and picks another from the bag, the probability that he will pick a green marble decreases.
d. The probability that Ryan will pick a red marble on the first try is 67%. If he keeps this marble and picks another from the bag, the probability that he will pick a green marble increases.
Answers
Answer:
C
Step-by-step explanation:
The probability Ryan will pick a red marble on the first try is 33%. If he keeps this marble and picks another from the bag, that % will decrease.
The probability of picking a red marble on the first try is 33%, and if Ryan keeps this marble and picks another from the bag, the probability of picking a green marble decreases.
Thus, option (C) is correct.
In this case, there are 20 red marbles out of a total of 60 marbles.
So the probability of picking a red marble on the first try is 20/60, which simplifies to 1/3 or 33%.
If Ryan keeps the red marble and picks another one from the bag, the total number of marbles becomes 59.
The number of green marbles remains the same at 40.
Therefore, the probability of picking a green marble on the second try is 40/59, which is less than the probability of picking a green marble on the first try.
Hence, the probability of picking a red marble on the first try is 33%.
Thus, option (C) is correct.
Learn more about Probability here:
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I need help with #3. Please help. I have to show all work so please explain
Answers
Answer:
a = 2
Step-by-step explanation:
Use Pythagorean Theorem:
[tex]a^2+b^2=c^2\\a^2+2.1^2=2.9^2\\a^2+4.41=8.41\\a^2=4\\\sqrt{a^2}=\sqrt{4}\\a=2[/tex]
Therefore, a is 2 meters.
Solve the inequality −14z<−37, and write the solution in interval notation.
Answers
Answer:
z is greater than 27/14
z € ( 37/14 ∞)
please help! (listing BRAINLIST and giving points) :D
Answers
Answer:
x = 50 + 95 = 145
.........
Answer:
x = 145°
Step-by-step explanation:
Given,
Measure of the first angle = 50°
Measure of the second angle = 95°
We know,
Sum of 3 angles of a triangle is equals to 180°
∴ The third angle = 180° - (50+95)°
= 180° - 145°
= 35°
Again,
Straight angle = 180°
∴ x = 180° - 35°
= 145°
∴x = 145°
An angle whose measure is - 102° is in standard position in which quadrant does the terminal side of the angle fall?
O Quadrant
O Quadrant il
Quadrant III
O Quadrant IV
Answers
Kevin was asked to determine the length of side XZ. His work is shown.
Which error did Kevin make?
Answers
Answer:
A.// He has the side lengths in the wrong place in the cosine ratio.
Step-by-step explanation:
ebsites
John has a bag of red and blue marbles. John chooses 2 marbles without replacing the first. Let A be the event where the first marble chosen
is red. Let B be the event where the second marble chosen is blue.
Which statement explains what the equation P (BA) = 0.6 means for these events?
A. The probability of choosing a blue marble after any marble has been removed is 0.6.
OB. The probability of choosing a red marble after a blue marble has been removed is 0.6.
O O O
C. The probability of choosing a blue marble after a red marble has been removed is 0.6.
OD. The probability of choosing a blue marble is 0.6, regardless of what else has been chosen.
Answers
Answer:
C. The probability of choosing a blue marble after a red marble has been removed is 0.6.
Step-by-step explanation:
P(B|A)
P(B|A) states the probability of event B happening, given that event A has happened.
In this question:
Event A: First marble is red.
Event B: Second marble is blue.
P(B|A) = 0.6
This means that the probability that the second marble is blue, considering that the first marble was red, is of 0.6, and thus, the correct answer is given by option C.
Choose the linear inequality that describes the graph the grey area represents the shaded region
Answers
Answer:
Explain to me how you expect anyone to do this,
as you haven't provided the graph or the inequalities.
Step-by-step explanation:
In ΔDEF, d = 440 inches, f = 410 inches and ∠F=120°. Find all possible values of ∠D, to the nearest 10th of a degree.
Answers
There are two solutions for the triangle DEF: ∠ D₁ ≈ 68.3°, ∠ D₂ ≈ 111.7°.
How to find all possible values of a triangle by law of sinesIn this question we have a triangle with two known sides and a known angle. By the law of sines we find the possible values of the angle D:
410/sin 120° = 440/sin D
Please notice that the sum of the internal angles of triangles equals 180°. Then,
sin D = (440/410) · sin 120°
sin D ≈ 0.929
There are two solutions for the triangle DEF: ∠ D₁ ≈ 68.3°, ∠ D₂ ≈ 111.7°.
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find the slope of the graph
Answers
Answer:
We count across to 4 on y axis = 2
and count down from 4 to -2 on x axis = -6
-6/2 = -3
m = -3
We know its minus because the reciprocal is the perpendicular imaginary line and if -3 is for the descending line then any ascending perpendicular line would show m = -1/-3 = 3
Step-by-step explanation:
Help ASAP pls I will give brainlist
Answers
Answer:
Step-by-step explanation:
There is a issue here...
is the spotted blue section considered "a blue sector"?
Assuming that "blue" or "red" is only a solid blue or red, this is the answer...
1) (1/10)* (3/10) = .03
2) (3/10) * (3/10) = 9/100 = .09
3) (3/10) * (1/10) = 3/100 = .03
4) (4/10) * (3/10) = 12/100 = .12
if the spotted blue and the solid blue are considered blue then this would be the result ...
1) (1/10)* (3/10) = .03
2) (4/10) * (3/10) = 12/100 = .12
3) (3/10) * (1/10) = 3/100 = .03
4) (8/10) * (3/10) = 24/100 = .24
please help! (listing BRAINLIST and giving points) :D
Answers
X = 122 degree
Flora is baking a pie and a cake for her restaurant. She needs 1/6 cup flour for the pie crust and 3/5 cup flour for the cake's frosting. How much flour will she use to make both?
(Type a whole number, fraction, or mixed number)
Answers
According to a NY Times article on December 13, 2009, The average selling price of a 32-inch LCD TV was $600. Use the annual CPI values from your text to compute the cost of that same TV in 2010 dollars. Express your answer rounded to the nearest cent.
Answers
Answer:
Your answer should be 647.51
Explanation : the price was 215.949 in December, 2009.
the price was 233.049 in December, 2013.
divide 233.049 by 235.949 and got 1.079185363.
multiply that by 600 and got 647.5112179.
The cost of the TV in 2010 is $647.5
Calculations and ParametersGiven that the complete information contains the Consumer Price Index values:
To find the CPI,
CPI= [tex]\frac{C_t}{C_0}[/tex]
Where C_t= cost of the market basket in the current period
C_0 = cost of the market basket in the base period
In December 2009, the price was 215. 949
In December 2013, the price was 233.049
Hence,
215. 949/233.049
= 1.079185363.
Then we would multiply by the base selling price
[tex]1.079185363 * 600 = 647.5112179.[/tex].
Read more about the consumer price index here:
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A. 40
B. 60
C. 140
D. 80
Answers
Answer:
measure of 4=360-(100+120)
=360-220
=140
so option C is the answer
Answer:
D. 80 is your answer
Step-by-step explanation:
If ∠6 is 120 and ∠5 is 100 we see a pattern forming for example, if we divide 120 by 6 we get 20 this is the same for if we divide 100 by 5, we get 20. Now all we need to do for ∠4 is to multiply it by 20 = 80, which is your answer!
Have a great day and I hope this helps!
8b - 5a + 4 for a = -4 and b = 7
If anyone gets this tysm
Answers
Answer:
80Step-by-step explanation:
Given Question,
8b - 5a + 4
Given Values:
a = -4 and b = 7
Solution,
8(7) - 5(-4) + 4
= 56 + 20 + 4
= 80 (Ans)
Answer:
80
Step-by-step explanation:
8b - 5a + 4
a = - 4
b = 7
8(7) - 5(- 4) + 4
56 - (- 20) + 4
56 + 20 + 4
60 + 20
80
A group of 12 friends bought tickets for an afternoon concert. However, not all of the friends were able to sit together. Tickets for floor seats cost $15 each, and tickets for tier seats cost $70 each. The total cost of the tickets was $345. How many tickets for tier seats did they purchase
Answers
Answer:
3 tier seats tickets
Step-by-step explanation:
Let the friends that bought floor seats be x and let the friends that bought tier seats be y.
Thus;
x + y = 12 - - - (eq 1)
Floor seats tickets cost $15 each, and tier seats tickets cost $70 each. The total cost of the tickets was $345. Thus;
15x + 70y = 345 - - - (eq 2)
Let's make x the subject in eq (1)
x = 12 - y
Putting this for x in eq 2 gives;
15(12 - y) + 70y = 345
180 - 15y + 70y = 345
55y = 345 - 180
55y = 165
y = 165/55
y = 3
Put 3 for y in x = 12 - y to get;
x = 12 - 3
x = 9
Thus, they purchased 9 floor seats tickets and 3 tier seats tickets
There are approximately 1.2×10 to the eighth household in the US if the average household uses 400 gallons of water each day what is the total number of gallons of water used by households in the US each day
Answers
Answer:
[tex]Total = 4.8 * 10^{10}[/tex]
Step-by-step explanation:
Given
[tex]h = 1.2 * 10^8[/tex] --- households
[tex]g = 400[/tex] --- gallons
Required
The number of households
To do this, we simply multiply the average households by the gallons.
[tex]Total = g* h[/tex]
[tex]Total = 400 * 1.2 * 10^8[/tex]
[tex]Total = 480 * 10^8[/tex]
Rewrite as:
[tex]Total = 4.8 * 10^2 * 10^8[/tex]
[tex]Total = 4.8 * 10^{10}[/tex]
WILL MARK BRAINLIEST PLEASE HELP
a survey of boys and girls in second grade was conducted asking whether or not they like pizza. The partially completed two-way table shows results of the survey. How many boys were included in the survey?
Answers
so there were 29 boys included in the survey
Step-by-step explanation:
answer is in the above photo
there are 29 boys total
Question 2
Find the volume.
Answers
Answer:
It is D...........nnnnnnn
Destiny has borrowed $8 from 7 different friends. Write an integer that
represents Destiny's total debt to her friends.
Answers
Answer:
56
Step-by-step explanation:
7×8=56
Hope this helps! :)
Sydney is cutting the crust from the edges of her sandwich. The dimensions, in centimeters, of the sandwich is shown.
Answers
Answer:
The answer is B) x = 8x² + 34; 45.52 centemiters
Step-by-step explanation:
Can y’all help me on question 11?!
Answers
Answer:
The correct answer is choice C.
Step-by-step explanation:
To find the area of the arrow, we must add together the areas of the rectangle and the triangle that make up the arrow. The rectangle has a length of 10 inches and a width of 4 inches, and the triangle has a base of 8 inches and a height of 2 inches. Using this information, we can plug numbers into the following formula:
Area of arrow = area of rectangle + area of triangle
Area of arrow = (10*4)+(1/2*8*2)
Area of arrow = 40 inches squared + 8 inches squared
Area of arrow = 48 inches squared
Therefore, the correct answer is option C, 48 square units (in this case, inches).
Hope this helps!
The summit of a volcano is 5 kilometers (km) above sea level, as shown below.
If the ocean floor has an elevation of -5 kilometers, which statement describes
the distance of the summit and the ocean floor?
It's not 0 or 5
Answers
Which of the following is equal to the rational expression
below when x+2 or 9?
4(x - 2)
(x - 2)(x-9)
Answers
Answer:4/x-9
Step-by-step explanation:
Помогите пожалуйста
y= sinx/cosx ; y=?
Answers
Answer:
[tex]\frac{1}{cos^2x}[/tex]
Step-by-step explanation:
[tex]y'=\frac{(sinx)'*cosx-(cosx)'*sinx}{cos^2x}=\frac{1}{cos^2x}.[/tex]
What is the area of this???
Answers
I think so