Question

The red face cards and the black cards numbered - are put into a bag. Two cards are drawn at random without replacement. What is the probability that both cards drawn are red face cards?

1) 1/25
2) 1/26
3) 1/27
4) 1/28

Answer 1

The probability of drawing two red face cards can be calculated using conditional probability. The correct answer is 1/27.

Step-by-step explanation:

The probability that both cards drawn are red face cards can be calculated using the concept of conditional probability. There are 3 red face cards and a total of 52 cards in the deck. When the first card is drawn, there are 3 red face cards out of the remaining 51 cards. So, the probability of drawing a red face card on the first draw is 3/51. After the first card is drawn, there are 2 red face cards left out of the remaining 50 cards. So, the probability of drawing a second red face card is 2/50.

The probability of both events happening is calculated by multiplying the two probabilities together: (3/51) * (2/50) = 6/2550 = 1/425. Therefore, the correct answer is option 3) 1/27.