Question

question 36 (1 point) saved a card is drawn at random from a standard 52 - card deck. refer to exhibit 7 - 9. the conditional probability that the card is a king given that a face card (jack, queen, or king) was drawn is question 37 (1 point) saved a soft drink company holds a contest in which a prize may be revealed on the inside of the bottle cap. the probability that each bottle cap reveals a prize is 0.2 and winning is independent from one bottle to the next. what is the probability that a customer must open three or more bottles before winning a prize?

Explanation:

Step1: Identify total face - cards and Kings

In a standard 52 - card deck, there are 12 face - cards (4 Jacks, 4 Queens, and 4 Kings). The number of Kings is 4.

Step2: Calculate conditional probability

The formula for conditional probability $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In the case of "the probability that the card is a King given that it is a face - card", $A$ is the event of drawing a King and $B$ is the event of drawing a face - card. Since all Kings are face - cards, $P(A\cap B) = P(A)$. So $P(A|B)=\frac{n(A)}{n(B)}$, where $n(A)$ is the number of Kings and $n(B)$ is the number of face - cards. So $P=\frac{4}{12}=\frac{1}{3}\approx33.3\%$.

Answer:

33.3% (1/3)