Question:
A card from a pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn. What is the probability that they both are diamonds
Answer:
Total number of cards = 52 and one card is lost.
Case 1: if lost card is a diamond card
Total number of cards = 51
Number of diamond cards = 12
Now two cards are drawn.
P(both cards are diamonds) = 12C2 / 51C2
Total number of cards = 52 and one card is lost.
Case 2: If lost card is not a diamond card
Total number of cards = 51
Number of diamond cards = 13
Now two cards are drawn.
P(both cards are diamonds) = 13C2 / 51C2
Now probability that both cards are diamond = 12C2 / 51C2 + 13C2 / 51C2
= (12C2 + 13C2 ) / 51C2
= {(12*11)/(2*1) + (13*12)/(2*1)}/{(51*50)/(2*1)}
= (12*11 + 13*12)/(51*50)
= (132 + 156)/2550
= 288/2550
= 96/850 (288 and 2550 divided by 3)
= 48/425 (96 and 850 divided by 2)
So probability that both cards are diamond is 48/425
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