Question

Jessa and Jana have an equal probability of becoming a captain of the volleyball team. Their coach decides that there is a 12% chance that he will pick both of them to be captains. There is a 44% chance that he will pick either Jessa or Jana to be a captain. Which of the following statements is true?

A. There is a 16% chance that Jessa will be a captain.
B. There is a 28% chance that Jana will be a captain.
C. There is a 32% chance that Jessa will be a captain.
D. There is a 56% chance that Jana will be a captain.​

Answer 1

A 36% chance but my English is not the best

Answer 2

Answer: B. There is a 28% chance that Jana will be a captain.

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Step-by-step explanation:

Lets define the following events

A = Jessa becomes captain

B = Jana becomes captain

Notation like P(A) refers to "the probability event A happens", which in this context means "the probability Jessa becomes captain". A similar situation happens with P(B).

P(A or B) = 0.44 is the probability either is selected (or both)

P(A and B) = 0.12 is the probability they are both selected

P(A or B) = P(A) + P(B) - P(A and B)

0.44 = P(A) + P(B) - 0.12

P(A) + P(B) = 0.44+0.12

P(A) + P(B) = 0.56

Recall that the first sentence states "Jessa and Jana have an equal probability of becoming a captain of the volleyball team."

Therefore, P(A) = P(B) and...

P(A) + P(B) = 0.56

P(A) + P(A) = 0.56

2*P(A) = 0.56

P(A) = 0.56/2

P(A) = 0.28

Both have an equal 28% chance of being picked.

This is why we go for choice B as the final answer.