you pick a card at random. without putting the first card back, you pick a second card at random.\nwhat is…

you pick a card at random. without putting the first card back, you pick a second card at random.\nwhat is the probability of picking a prime number and then picking a prime number?\nwrite your answer as a decimal rounded to the nearest thousandth.

you pick a card at random. without putting the first card back, you pick a second card at random.\nwhat is the probability of picking a prime number and then picking a prime number?\nwrite your answer as a decimal rounded to the nearest thousandth.

Answer

Explanation:

Step1: Count prime - numbered cards

The prime - numbered cards among 3, 4, 5, 6, 7, 8, 9 are 3, 5, 7. So there are 3 prime - numbered cards out of 7 cards initially. The probability of picking a prime - numbered card on the first draw, $P_1=\frac{3}{7}$.

Step2: Calculate the probability of the second draw

Since the first card is not replaced, there are 6 cards left. If the first card was prime, then there are 2 prime - numbered cards left. The probability of picking a prime - numbered card on the second draw given that the first card was prime, $P_2=\frac{2}{6}=\frac{1}{3}$.

Step3: Use the multiplication rule for dependent events

The probability of both events occurring is $P = P_1\times P_2$. $P=\frac{3}{7}\times\frac{1}{3}=\frac{3\times1}{7\times3}=\frac{1}{7}\approx0.143$.

Answer:

0.143