Question

Without replacement, what is the probability that

a) first card drawn is a jack, and the second card drawn is a queen

b) both cards drawn are red

Answer 1

Solution:

Given: Two cards are drawn without replacement.

Part a) Find:

P( first card drawn is a jack, and the second card drawn is a queen) =............?

We have total cards = n = 52

We have 4 Jack cards and 4 Queen cards.

Thus drawing first jack card has 4/52 probability. Since we are not replacing first drawn card we have total 51 cards for second draw

thus we have 4/51 probability for second card as queen.

Thus

P( first card drawn is a jack, and the second card drawn is a queen) = 4/52 X 4/51

P( first card drawn is a jack, and the second card drawn is a queen) = (1/13) X (4/51)

P( first card drawn is a jack, and the second card drawn is a queen) = (1X4) / ( 13 X 51)

P( first card drawn is a jack, and the second card drawn is a queen) = 4 / 663

P( first card drawn is a jack, and the second card drawn is a queen) = 0.006033

Part b) Find:

P(  both cards drawn are red) =.........?

We have total 26 red cards.

Thus

P(  both cards drawn are red) = P( First Red and Second red)

P(  both cards drawn are red) = (26/52) X ( 25/51)

( Since for second draw we have 25 red cards and total 51 cards)

P(  both cards drawn are red) = (1/2) X ( 25/51)

P(  both cards drawn are red) = (1X 25) X ( 2 X 51)

P(  both cards drawn are red) = 25 / 102

P(  both cards drawn are red) = 0.245098

( Round answer to specified number of decimal places)