Question

A deck contains 11 cards numbered 1 through 11. A card is randomly selected and reinserted into the deck. The deck is shuffled. Then another random selection is made. Events Event A: The first selection is a 4. Event B: The second selection 0 is a 3.

Answer 1

the probability of both events happening, selecting a 4 on the first draw and a 3 on the second draw, is 1/121.

Explanation:

Since the card is reinserted and the deck is shuffled after the first selection, the probability of selecting any card on the second draw is the same as the probability of selecting any card on the first draw. Therefore, the two events are independent.

The probability of Event A, selecting a 4 on the first draw, is 1/11, since there is one 4 out of the 11 cards in the deck.

The probability of Event B, selecting a 3 on the second draw, is also 1/11, since the deck is reshuffled and the probability of selecting any card is the same.

The probability of both events happening is the product of their probabilities:

P(A and B) = P(A) x P(B)

P(A and B) = (1/11) x (1/11)

P(A and B) = 1/121

Therefore, the probability of both events happening, selecting a 4 on the first draw and a 3 on the second draw, is 1/121.