Question

suppose that a single card is selected from a standard 52 - card deck. what is the probability that the card drawn is a queen? now suppose that a single card is drawn from a standard 52 - card deck, but it is told that the card is a face card (jack, queen, or king). what is the probability that the card drawn is a queen? the probability that the card drawn from a standard 52 - card deck is a queen is 0.077 (round to three decimal places as needed.) the probability that the card drawn from a standard 52 - card deck is a queen, given that this card is a face card, is (round to three decimal places as needed.)

Explanation:

Step1: Calculate probability of drawing a queen from 52 - card deck

There are 4 queens in a 52 - card deck. The probability formula is $P(A)=\frac{n(A)}{n(S)}$, where $n(A)$ is the number of favorable outcomes and $n(S)$ is the total number of outcomes. So $P(\text{queen})=\frac{4}{52}=\frac{1}{13}\approx0.077$.

Step2: Calculate conditional probability

There are 12 face - cards (4 jacks, 4 queens, 4 kings) in a 52 - card deck. The number of favorable outcomes (queens among face - cards) is 4, and the number of total face - cards is 12. Using the conditional probability formula for events $A$ (drawing a queen) and $B$ (drawing a face - card), $P(A|B)=\frac{n(A\cap B)}{n(B)}$. Here, $A\cap B$ is the event of drawing a queen (since all queens are face - cards), so $P(\text{queen}|\text{face - card})=\frac{4}{12}=\frac{1}{3}\approx0.333$.

Answer:

0.333