Question

Two cards are drawn without relplacement from a shuffled deck of 52 cards. Determine the probability of each event.

a)The first card is a heart and the second card is Q of hearts.

P(BlA)=P(A&B)/P(A)
(13/52)(1/51)/(1/4) = 1/51

How is this method incorrect?

Answer 1

I don't see why you are using the Conditional probability formula on this one.
you want the event to happen in a specific order, namely
one of the non-queen hearts, and then the queen of hearts.
so
prob = 12/52 * 1/51 = 1/121

Answer 2

In order for the second card to be the queen of hearts, the first card must be some other heart, and that has a probability of 12/52 = 3/13. Multiply that by the prob. of getting QH on the next draw, which is 1/51, and you get
3/663 = 1/221

Whatever you are doing with Bayesian probabilities P(B|A), etc., is wrong.

1/51 is the probability of getting QH on the second draw, after getting ANYTHING ELSE on the first draw.

Answer 3

I was just taught this formula so I thought I'd use it, since one event comes after another.

Thank you.