Suppose that two cards are randomly selected from a standard 52-card deck. A) Wh

Question

Suppose that two cards are randomly selected from a standard 52-card deck. A) What is the probability that the first card is a spade and the second card is a spade if the sampling is done without replacement?
B) What is the probability that the first card is a spade and the second card is a spade if the sampling is done with replacement? Suppose that two cards are randomly selected from a standard 52-card deck. A) What is the probability that the first card is a spade and the second card is a spade if the sampling is done without replacement?
B) What is the probability that the first card is a spade and the second card is a spade if the sampling is done with replacement? A) What is the probability that the first card is a spade and the second card is a spade if the sampling is done without replacement?
B) What is the probability that the first card is a spade and the second card is a spade if the sampling is done with replacement?

Explanation / Answer

a) Prob that the first card is a spade = 1/4

Without replacement hence Prob for second card to be spade = 12/51

Hence reqd prob = 13C2/52C2 = 13(12)/52(51) =

0.05882

b) If with replacement Prob for I and ii card being spade is equal = 1/4

Hence required prob = 1/16 = 0.0625

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