Question

question 35 (1 point) saved exhibit 7 - 8 a standard 52 - card deck is shuffled and 2 cards are picked from the top of the deck. refer to exhibit 7 - 8. the probability that the first card is a face card (jack, queen, king) and the second card is not a face card is 5.3% 17.8% 18.1% 59.2%

Explanation:

Step1: Calculate probability of first - card being face - card

There are 12 face - cards (4 Jacks, 4 Queens, 4 Kings) in a 52 - card deck. The probability of the first card being a face - card is $P_1=\frac{12}{52}=\frac{3}{13}$.

Step2: Calculate probability of second - card not being face - card given first is face - card

After picking a face - card first, there are 51 cards left, and $52 - 12=40$ non - face cards left. So the probability of the second card not being a face - card given the first is a face - card is $P_2=\frac{40}{51}$.

Step3: Calculate combined probability

Since these are independent events in the sense of sequential drawing, the probability of both events happening is the product of their probabilities. So $P = P_1\times P_2=\frac{3}{13}\times\frac{40}{51}=\frac{120}{663}\approx 0.181 = 18.1\%$.

Answer:

18.1%