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Question

3 cards are given, one of them is red on both sides, one is blue on both sides & one is blue on one side red on the other side. One of them is chosen randomly & put on the table. It shows red colour on the upper side. The chance of the other side of the card being red is:

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Solution

Let E1,E2,E3 be the event of choosing a card red on both sides , card blue on both sides and blue on side & red on other side
Let A be the event that the drawn card shows red on upper side .
then , P(AE1)=22=1
P(AE2)=02=0
P(AE3)=12
P(E1)=P(E2)=P(E3)=13
P(E1A)=P(E1)×P(AE1)P(E1)×P(AE1)+P(E2)×P(AE2)+P(E3)×P(AE3)
=13×113×1+13×0+13×12
=2626+16
=23

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