Question

1. Suppose you draw two cards from a deck of 52 cards without replacement.

a. What’s the probability that the first draw is a heart and the second draw is not a heart?

b. What’s the probability that exactly one of the cards are hearts?

c. If you draw two cards with replacement, what’s the probability that none of the cards are hearts?

Answer 1

1a) Total 52 cards out of which 13 cards of heart cards, so 39 cards are of no hearts.

P(1st heart, 2nd not heart) =

This is without replacement that's why in the second card turn total number of cards is 51.

1b) P(exactly one card is hearts) = P(1st card is heart) + P(2nd card is heart)

1c) This is with replacement.

P(none of the cards are hearts) = P(both not hearts) =

Please comment if any doubt. Thank you.