How do I solve this problem?

Question

you are dealt two cards successively without replacement from a shuffled deck of 52 playing cards. find the probability that the first card is a heart and the second card is a diamond. round to nearest thousandth

Answer 1

H₁ = picking a first card that is a heart

D₂ = picking a second card that is a diamond

P(H₁) = 13/52 = 1/4

P(D₂) = 13/51

P(H₁ ∩ D₂) = (1/4)*(13/51) = 13/204 = 0.064

The probability that the first card is a heart and the second card is a diamond, without replacement, is 0.064.