Question

A card are chosen from a deck of 52 playing card. It is replace and a second card is chosen. What is the probabitily that both cards are clubs

Answer 1

there are 13 cards out of 52 that are clubs, so the probability of drawing a club out of a full deck is 1/4.

If the card is replaced and a second random draw is made, clubs will be chosen with the same probability of 1/4.

The probabilities for two independent events occuring in a row multiply, so the probability for these two cards (with replacement) to be clubs is p = 1/4* 1/4 = 1/16

If you prefer counting instead of probabilities, you can think if the same problem as follows:

how many choices are there to draw two clubs in a row: 1

how many choices are there to draw any suit followed by any suit: 4x4=16

so the final prob is 1/16