Question

If two cards are drawn without replacement from a 52 card deck, find the probability that the second card drawn is red, given that the first card was a heart.

Answer 1

The probability that the second card drawn is red, given that the first card was a heart is 0.1225

Explanation:

Total cards in a deck = 52

Total red cards = 26

Heart cards = 13

Probability of getting red card =
`(13)/(52)`

Total remaining card = 51

Remaining red cards = 25

Probability of getting red card in second draw without replacement =
`(25)/(51)`

So, the probability that the second card drawn is red, given that the first card was a heart =
`(13)/(52) * (25)/(51) =0.1225`

Hence the probability that the second card drawn is red, given that the first card was a heart is 0.1225