A person chooses two cards from a thoroughly shuffled deck, and then he rolls a die. If he does not put the first card back in the deck before he draws the next, what is the probability that the first card is a queen, the second card is a jack, and the die shows a 5?

Answer 1

The probability of the first card being a queen is 4/52, since there are 4 queens in a deck of 52 cards.

After the first card is drawn, the deck will have 51 cards, among which there are 4 jacks, so the probability of drawing a jack as the second card is 4/51.

The probability of rolling a 5 on a die is 1/6.

Since these three events are independent, the probability of all three happening together is the product of their individual probabilities:

(4/52) * (4/51) * (1/6) = 1/663

Therefore, the probability that the first card is a queen, the second card is a jack, and the die shows a 5 is 1/663.

Answer 2

very strange result by the bot.

It got it right up to
(4/52) * (4/51) * (1/6)
but then couldn't do the basic arithmetic.

(4/52) * (4/51) * (1/6) = 2/1989 , not 1/663