If there is a deck of cards containing 2 red cards, 3 blue cards, 4 green cards, and 1 yellow card, what is the probability of choosing a red card,...

Hello!

You should multiply these probabilities (you computed them correctly). So the answer is `2/10*3/9 = 1/5*1/3 = 1/15.`

This comes from the formula of the conditional probability,

`P(A | B) = (P(A and B)) / (P(B)),`

where `A | B` is the event "A given B", which means event A after it is known that the event B has occurred.

In our problem, B is the event "the first card is red" and A is "the second card is blue". Then `(A and B)` means "the first card is red AND the second card is blue", `(A|B)` means "the second card will be blue after it is known that the first card was red".

Obviously `P(B) = 2/10=1/5` and `P(A|B) = 3/9=1/3,` so `P(A and B)=P(A|B)*P(B)=1/15.`