Question

In a standard 52-card deck, half of the cards are red and half are black. The 52 cards are divided evenly into 4 suits: spades, hearts, diamonds, and clubs. Each suit has three face cards (jack, queen, king), and an ace. Each suit also has 9 cards numbered from 2 to 10. 7.

Dawn draws 1 card, replaces it, and draws another card. Is it more likely that she draws 2 red cards or 2 face cards?​

Answer 1

It is more likely she draws 2 red cards

Explanation:

Given that:

Number of red d cards in deck = 26

Number of face cards = 4 * 3 = 12 face cards

If two cards are drawn with replacement ;

Probability = (required outcome / Total possible outcomes)

P(1st card red) = 26 /52) = 1/2

P(2nd card red) = 26 /52 = 1/2

P(1st card red) * P(2nd card red)

1/2 * 1/2 = 1/4 = 0.25

P(1st card face card) = 12/52 = 3/13

P(2nd card, face card) = 12/52 = 3/13

P(1st card face card) * P(2nd card face card)

3/13 * 3 /13 = 9/169 = 0.053

0.25 > 0.053

It is more likely she draws 2 red cards