Question

Two cards are drawn with replacement, one after the other, and the outcomes recorded. What is the probability that at least one of the two cards is a face card (Jack, Queen, or King)? (Give the answer as a decimal rounded to three decimal places.)

Answer 1

The probability of drawing at least one face card when drawing two cards with replacement from a standard deck is approximately 0.407.

Step-by-step explanation:

The student is asking for the probability of drawing at least one face card (Jack, Queen, or King) when drawing two cards with replacement from a standard deck of 52 cards. To find this, we can use the complement rule: subtract the probability of not drawing a face card in both draws from 1. There are 12 face cards in a deck of 52 cards, so the probability of drawing a non-face card (event N) on one draw is 40/52 (since there are 40 non-face cards).

Using the complement rule:

1. Calculate the probability of drawing a non-face card both times: P(NN) = (40/52) * (40/52).
2. Subtract the above probability from 1 to get the probability of at least one face card: P(at least one F) = 1 - P(NN).

Now perform the calculations:

P(NN) = (40/52) * (40/52) = 0.5929 (approximately).

P(at least one F) = 1 - 0.5929 = 0.4071 (rounded to three decimal places).

Therefore, the probability of drawing at least one face card in two draws with replacement is approximately 0.407.