Daniel plays two games in the casino. The first game he believes he has 60% chance to win. If he wins the first game, he will win the second game with 25% chance, if he loses the first game, he will win the second game with 75% chance. The winning prices for the first and second game are $1 and $2 respectively
A. What is the probability that he wins the second game?
B. If he wins the second game, what is the probability that he also won the first game?
C. What is the expected value for the price he wins from the two games? What is the variance of it?
Answers
Answer:
1) the probability that he wins the second game is 0.45
2) the probability he wins the first game given that he won the second game is 0.333
3) Expected Value is $ 1.5 and the variance is 0.75
Step-by-step explanation:
Given the data in the question;
Let Win1 represent first game victory
and Loss1 represent first game loss
Let Win2 denote second game victory
and Loss2 denote second game loss
now from the Tree diagram of Daniel;
P ( Win1 ) = 0.6
P ( Loss1 ) = 0.4
P ( Win2 | Win1 ) = 0.25
P ( Loss2 | Win1 ) = 0.75
P ( Win2 | Loss1 ) = 0.75
P ( Loss2 | Loss1 ) = 0.25
1) probability that he wins the second game will be;
P ( Win2 ) = [P ( Win1 ) × P ( Win2 | Win1 )] + [P ( Loss1 ) × P ( Win2 | Loss1 ) ]
we substitute
= [0.6 × 0.25] + [0.4 * 0.75] = 0.45
Therefore the probability that he wins the second game is 0.45
2)
If he wins the second game, what is the probability that he also won the first game will be;
{From Bayes' Theorem}
P ( Win1 | Win2 ) = P ( Win1 ) × P ( Win2 | Win1 ) / P ( Win2 )
= 0.6 × 0.25 / 0.45 = 0.333
Therefore the probability he wins the first game given that he won the second game is 0.333
c)
winnings probability
$0 0.4 × 0.25 = 0.1
$1 0.6 × 0.75 = 0.45
$2 0.4 × 0.75 = 0.3
$3 0.6 × 0.25 = 0.15
so Expected Value = ∑( winnings × individual win probability)
= (0 × 0.1) + (1 × 0.45) + (2 × 0.3) + (3 × 0.15)
= 0 + 0.45 + 0.6 + 0.45
= $ 1.5
Variance = ∑( X² ) - (∑(X))²
∑( X² ) = Summation of ( Winnings² × Probability of Each Win )
so
Variance = 0 × 0 × 0.1 + 1 × 1 × 0.45 + 2 × 2 × 0.3 + 3 × 3 × 0.15 - ( 1.5 )²
Variance = 0 + 0.45 + 1.2 + 1.35 - 2.25
Variance = 3 - 2.25
Variance = 0.75
Therefore Expected Value is $ 1.5 and the variance is 0.75
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[tex]\frac{5}{4}[/tex] [tex]or[/tex] [tex]1.25[/tex]
Step-by-step explanation:
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Answer:
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4
ОООО
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36
Answers
Answer:
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Step-by-step explanation:
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Answers
How do you round to the ones place?
Look to the next smallest place value, the digit to the right of the place value you're rounding to. For example, if you want to round to the nearest ten you'd look at the ones place. If the digit in the next smallest place value is less than five (0, 1, 2, 3, or 4), you leave the digit you want to round to as-is.
Answer:
Step-by-step explanation:
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Step-by-step explanation:
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Answer:
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Answers
Answer:
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Answers
Answer:
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Answer:
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Step-by-step explanation:
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Answers
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Answers
Answer:
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Answers
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Step-by-step explanation:
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Step-by-step explanation:
Explanation:-
From graph The centre of the circle C( -5 , -7)
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Answers
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Answers
Answer:
$90
Step-by-step explanation:
To find the original price, divide 63 by 0.7:
63/0.7
= 90
So, the original price is $90
Answer:
$90.00
Step-by-step explanation:
First of all let x be the price of the pair of shoes that you are trying to find.
next since we have 30percent off that price we have
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Answers
Answer:
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Step-by-step explanation:
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ООО
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Step-by-step explanation:
The answer is on the bottom if you just wanna scroll down.
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Answer:
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Answers
Answer:
A.
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Answer:
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Step-by-step explanation:
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<
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Answer:
b
Step-by-step explanation:
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Answers
Answer:
4
Step-by-step explanation:
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Answers
Answer:
IN THIS ORDER
NO
NO
YES
YES
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Step-by-step explanation:
Hope this helped if I got it wrong, sorry ill edit it if I did :)