A bowl of fruit contains 5 bananas, 6 oranges, and 3 apples. Two fruits are selected...

A bowl of fruit contains 5 bananas, 6 oranges, and 3 apples. Two fruits are selected one after another without replacement. What is the probability that the second fruit drawn is an apple given the first fruit drawn was a banana?

My answer is (ba)+(oa)+(aa) / (bb) + (bo) + (ba) which is wrong.. why?

Expert Solution

P(A | B) = P(A and B) / P(B)

P(second fruit is an apple | first fruit is banana) = P(first fruit is banana and second fruit is an apple) / P(first fruit is banana)

= ((ba)) / ((bb) + (bo) + (ba))

= (5/14 * 3/13) / [(5/14 * 4/13) + (5/14 * 6/13) + (5/14 * 3/13)]

= (15/182) / (65/182)

= 15/65

= 3/13

orchestra answered 1 year ago

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