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CBSE Class 12-science Answered

Two cards from a pack of 52 cards are lost . From the remaining 50 cards , one card is drawn . If the drawn card is a spade , what is the probability that lost cards were both spades ? 
Asked by abhitailor158 | 17 Mar, 2019, 12:12: PM
answered-by-expert Expert Answer
There are three possible events
 
(1) Both the lost cards are spade . Let this event be E1 . probability of this event ,  p( E1 ) = (13/52) (12/51)
 
(2) one lost card is spade and other one is not spade. Let this event be E2 . Probability of this event,
 
                     p( E2 ) = (13/52) (39/51) + (39/52) (13/51) = (26×39) / (52 × 51 )
 
(3) both the lost cards are not spade. Let this event be E3 . probability of this event, p(E3 ) = (39/52) (38/51)
 
probability of getting spade from 50 cards , when both lost cards are spade ,  p(S/E1 ) = 11/50
 
probability of getting spade from 50 cards , when one lost card is spade and other one is not a spade,  p(S/E2 ) = 12/50
 
probability of getting spade from 50 cards , when both lost cards are not spade ,  p(S/E3 ) = 13/50
 
If spade is selected from 50 cards after two cards were lost,
then the probability that two lost cards are spade is  p(E1 / S ) and it is obtained by applying Bayes theorem
 
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Answered by Thiyagarajan K | 17 Mar, 2019, 10:51: PM

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