Question

1. a drawer contains 10 red socks, 7 blue socks, and 12 green socks. suppose you select a sock at random from the drawer, do not replace it, and then select another sock. what is the probability that the first sock is red and the second sock is green? 75.9% 77.3% 14.3% 14.8%

Explanation:

Step1: Calculate total number of socks

Total socks = 10 (red)+7 (blue)+12 (green)=29

Step2: Calculate probability of first - red sock

Probability of first sock being red, $P(R_1)=\frac{10}{29}$

Step3: Calculate probability of second - green sock after first red

After taking out a red sock, there are 28 socks left. Probability of second sock being green given first is red, $P(G_2|R_1)=\frac{12}{28}$

Step4: Calculate joint probability

By the multiplication rule for dependent events $P(R_1\cap G_2)=P(R_1)\times P(G_2|R_1)=\frac{10}{29}\times\frac{12}{28}=\frac{120}{812}\approx 0.148 = 14.8\%$

Answer:

14.8%