Respuesta :
Answer:
d. 0.3056
Step-by-step explanation:
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
We have these following probabilities:
With the fair coin, a 50% probability of winning a prize.
With the biased coin, a 100-78 = 22% probability of winning a prize.
50% probability of choosing each coin.
What is the probability of choosing the biased coin if you won a prize.
Event A: Winning the prize:
Event B: Choosing the biased coin.
Probability of choosing the biased coin and winning the prize.
[tex]P(A \cap B) = 0.5*0.22 = 0.11[/tex]
Probability of winning the prize:
[tex]P(A) = 0.5*0.22 + 0.5*0.5 = 0.36[/tex]
Conditional probability:
[tex]P(B|A) = \frac{0.11}{0.36} = 0.3056[/tex]
So the correct answer is:
d. 0.3056
