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Question

A hat contains a number of cards with 30% white on both sides, 50% black on one side and white on the other side, 20% black on both sides. The cards are mixed up, and a single card is drawn at random and placed on the table. Its upper side shows up black. The probability that its other side is also back is

A
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C
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D
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Solution

The correct option is B
Let us consider the following events.
A : card shows up black
B1: card with both sides black
B2: card with both sides white
B3: card with one side white and one black
P(B1)=210,P(B2)=310.P(B3)=510P(AB1)=1,P(AB2)=0,P(AB3)=12P(B1A)=210×1210×1+310×(0)+510×12=44+5=49


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