Answer: Choice C) 0.4
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Explanation:
Define the two events as such
A = event of chosen to be in the play
B = event of getting the lead role
The probability of getting chosen in the play is 0.5, so P(A) = 0.5
Because getting a lead role means you must have been selected for the play, this means that event B depends entirely on event A. We can say
P(A and B) = 0.2
which is the same as P(B and A)
Therefore the conditional probability is
P(B given A) = P(B and A)/P(A)
P(B given A) = 0.2/0.5
P(B given A) = 2/5
P(B given A) = 0.4
You can replace each "given" with a vertical line to write P(B | A) instead of "P(B given A)". I used "given" because the vertical line could be easily mistaken for an uppercase letter i or a lowercase letter L.
