Questions: Two cards are selected from a standard deck of 52 playing cards. The first card is not replaced before the second card is selected. Find the probability of selecting a queen and then selecting a five. The probability of selecting a queen and then selecting a five is (Round to three decimal places as needed.)

Solution Steps

To find the probability of selecting a queen and then selecting a five from a standard deck of 52 playing cards without replacement, we need to follow these steps:

1. Calculate the probability of drawing a queen first.
2. Calculate the probability of drawing a five after a queen has already been drawn.
3. Multiply these probabilities together to get the final probability.

The probability of drawing a queen from a standard deck of 52 cards is given by:

\[ P(\text{Queen}) = \frac{\text{Number of Queens}}{\text{Total Cards}} = \frac{4}{52} = \frac{1}{13} \approx 0.0769 \]

After drawing a queen, there are 51 cards left in the deck. The probability of drawing a five from the remaining cards is:

\[ P(\text{Five | Queen}) = \frac{\text{Number of Fives}}{\text{Remaining Cards}} = \frac{4}{51} \approx 0.0784 \]

The total probability of drawing a queen first and then a five is the product of the two probabilities calculated above:

\[ P(\text{Queen and then Five}) = P(\text{Queen}) \times P(\text{Five | Queen}) = \frac{4}{52} \times \frac{4}{51} = \frac{16}{2652} \approx 0.0060 \]

Final Answer