Question

10. At a carnival you win a prize if you get a heads, you must first choose a coin. There is a fair and a biased coin, while choosing each coin is equally likely, the biased coin has a 78% of landing tails. What is the probability of choosing the biased coin if you won a prize. a. 0.2146 b. 0.4084 c. 0.3421 d. 0.3056 e. 0.2670

Answer 1

Answer:

d. 0.3056

Step-by-step explanation:

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ 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.

$P(A \cap B) = 0.5*0.22 = 0.11$

Probability of winning the prize:

$P(A) = 0.5*0.22 + 0.5*0.5 = 0.36$

Conditional probability:

$P(B|A) = \frac{0.11}{0.36} = 0.3056$

So the correct answer is:

d. 0.3056