Alice plays the following game with Bob. First, Alice randomly chooses a set of 4 cards out of a 52-card deck, memorizes them, and places them back into the deck. (Any set of 4 cards is equally likely.) Then, Bob randomly chooses 8 cards out of the same deck. (Any set of 8 cards is equally likely.)

What is the probability that all 4 cards Alice chose were also among the 8 cards chosen by Bob?

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Mathematics

13 August, 00:36

Alice plays the following game with Bob. First, Alice randomly chooses a set of 4 cards out of a 52-card deck, memorizes them, and places them back into the deck. (Any set of 4 cards is equally likely.) Then, Bob randomly chooses 8 cards out of the same deck. (Any set of 8 cards is equally likely.)

What is the probability that all 4 cards Alice chose were also among the 8 cards chosen by Bob?

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Belen · Answer 1

Choosing 8 cards out of a deck of 52 cards and that the order is not important can be determined through the equation,

52C8 = 752538150

If the four cards initially picked by Alice should be present, we take them as 1 whole set. Such that picking 8 cards would only give us 5 (1 set of 4 cards and 4 other cards). That is,

52C5 = 2598960

The probability is solved by dividing the latter by the former, giving us the answer of 56/16215 which is also equal to 0.00345