Question

Two cards are drawn one after the other from a pack of 52 cards with replacement. What is the probability that both the cards drawn are face cards?

Answer 1

Given:

A pack of 52 cards.

Two cards are drawn one after the other with replacement.

To Find:

The probability that both the cards drawn are face cards.

Solution:

A deck of 52 cards contain 12 face cards, jack, queen and king in 4 suites.

Therefore

• there is a 12/52 chance of drawing one face card at a time.

Now,

• Given that two cards are drawn one after the other, with replacement.

Therefore,

• Probability of drawing a face card first time = 12/52

Similarly,

• Probability of drawing a face card second time = 12/52

Therefore,

• probability that both the cards drawn are face cards = 12/52 x 12/52
• Probability = 3/13 x 3/13 = 9/169

The  probability that both the cards drawn are face cards  is 9/169.