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?
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.