Answer:
d. 0.3056
Step-by-step explanation:
We use the conditional probability formula to solve this question. It is
![P(B|A) = \frac{P(A \cap B)}{P(A)}](https://tex.z-dn.net/?f=P%28B%7CA%29%20%3D%20%5Cfrac%7BP%28A%20%5Ccap%20B%29%7D%7BP%28A%29%7D)
In which
P(B|A) is the probability of event B happening, given that A happened.
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.
![P(A \cap B) = 0.5*0.22 = 0.11](https://tex.z-dn.net/?f=P%28A%20%5Ccap%20B%29%20%3D%200.5%2A0.22%20%3D%200.11)
Probability of winning the prize:
Conditional probability:
![P(B|A) = \frac{0.11}{0.36} = 0.3056](https://tex.z-dn.net/?f=P%28B%7CA%29%20%3D%20%5Cfrac%7B0.11%7D%7B0.36%7D%20%3D%200.3056)
So the correct answer is:
d. 0.3056