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If I choose four cards from a standard -card deck,with replacement, what is the probability that I will end up with four cards from the same suit?

 Apr 20, 2022
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The first card can be any suit so we don't need to include it into the calculation.

 

Because each card is replaced after it is drawn, there is a 1/4th chance that the second card will match the first.

 

It is also true that the third card has a 1/4th chance that it will match the first two.

 

Lastly, the fourth card has a 1/4th chance that it will match the first three.

 

Multiplying together these possibilities, we get a probability of (1/4) x (1/4) x (1/4)  =  1/64.

 Apr 20, 2022

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