Question

From a standard of cards two cards are chosen without replacement one at a time.Find the probability of drawing a face card given that the first card was red. The answer is not correct, and the ones that are correct doesn't fully explain how they got the answer. Please, be very specific how to do each step, thank you so much.

Answer 1

Required probability = P(drawing the second card as a face card | the first card was red)

= P(drawing the second card as a face card and the first card was red) / P(the first card drawn was red)

Now, P(the first card drawn was red) =

{Since out of the 52 cards, 26 are red}

P(drawing the second card as a face card and the first card was red)

= P(drawing the second card as a face card and the first card was red and face card) + P(drawing the second card as a face card and the first card was red and not a face card)

=

{Face cards are : J, Q and K. So there are 12 face cards in a deck. Out of these face cards, 6 are red and 6 are black.

This also means that there are 20 black cards which are not face cards and 20 red cards which are not face cards.}