Questions: 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 (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.)

Solution Steps

To calculate the unconditional probability \(P(A)\) of drawing a specific type of card from the deck, we use the formula \(P(A) = \frac{n_{specific}}{N}\), where \(n_{specific}\) is the number of specific type cards in the deck and \(N\) is the total number of cards in the deck. Substituting the given values, we get \(P(A) = \frac{4}{52} = 0.077\).

To calculate the conditional probability \(P(A|B)\) of drawing a specific type of card given that the card is from a specific subset, we use the formula \(P(A|B) = \frac{n_{specific \cap subset}}{n_{subset}}\), where \(n_{specific \cap subset}\) is the number of that type of card within the subset and \(n_{subset}\) is the total number of cards in the subset. Since all specific type cards are included in the subset, \(n_{specific \cap subset} = n_{specific}\). Thus, \(P(A|B) = \frac{4}{12} = 0.333\).

Final Answer: