Shuffle a deck of cards and pick two cards at random. Observe the sequence of th

Question

Shuffle a deck of cards and pick two cards at random. Observe the sequence of the two cards in the order in which they were chosen. (a) How many outcomes are in the sample space? (b) How many outcomes are in the event that the two cards are the same type but different suits? (c) What is the probability that the two cards are the same type but different suits? (d) Suppose the experiment specifies observing the set of two cards without considering the order in which they are selected, and redo parts (a) - (c).

Explanation / Answer

A) Total no of outcomes in sample space = 52P2 = 52! / 50! = 52 * 51 = 2652

B) Total no of outcomes that the two cards are the same type but different suits = 52C1 * 3C1 = 52 * 3 = 156

C) The probability that the two cards are same type but different suits = 156 / 2652 = 0.06

D) Total no of sample space = 52C2 = 52! / (2! * 50!) = 52 * 51/ 2 = 1326

Probability that the two cards are the same type but different suits = 52C1 * 3C1 / 52C2 = 156 / 1326 = 0.12

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