Two cards are drawn together from a pack of 52 cards. The probability that one is a club and one is a diamond ?



Two cards are drawn together from a pack of 52 cards. The probability that one is a club and one is a diamond ?

A. 13/51

B. 1/52

C. 13/102

D. 1/26

Answer : C. 13/102...


Explanation:

    n(S) = Total number of ways of drawing 2 cards from 52 cards = 52C2.
    Let E = event of getting 1 club and 1 diamond.
    We know that there are 13 clubs and 13 diamonds in the total 52 cards.
    Hence, n(E) = Number of ways of drawing one club from 13 and one diamond from 13 = 13C1 × 13C1 = 13/102
    P(E) = n(E)/n(S)
    = (13C1 × 13C1) / 52C2
    = 13/102.


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