Question

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 jack and then selecting a queen. the probability of selecting a jack and then selecting a queen is 0.006. (round to three decimal places as needed.)

Explanation:

Step1: Calculate probability of selecting a jack first

There are 4 jacks in a 52 - card deck. So the probability of selecting a jack first, $P(J_1)=\frac{4}{52}=\frac{1}{13}$.

Step2: Calculate probability of selecting a queen second

Since the first card is not replaced, there are 51 cards left and 4 queens. So the probability of selecting a queen second given a jack was selected first, $P(Q_2|J_1)=\frac{4}{51}$.

Step3: Calculate the joint - probability

By the multiplication rule for dependent events $P(J_1\cap Q_2)=P(J_1)\times P(Q_2|J_1)$. Substitute the values: $P(J_1\cap Q_2)=\frac{1}{13}\times\frac{4}{51}=\frac{4}{663}\approx0.006$.

Answer:

$0.006$