Answer to Question #148248 in Statistics and Probability for Ella Ssebulime

Question

Natalie has 8 socks in a drawer. 5 of the socks are black. 3 of the socks are white. Natalie takes out a sock at random, writes down its color, and puts it back into the drawer. Then Natalie takes out a second sock, at random, and writes down its color. A)What is the probability that both socks are black? B)What is the probability that the first sock is black and the second sock is white? C)What is the probability that both socks are white) D What is the probability that the first sock is white and the second sock is black? E)What is the probability that the socks are the same color?

Answer 1

A)

$$P(BB)=\dfrac{5}{8}\times \dfrac{5}{8}=\dfrac{25}{64}$$

B)

$$P(BW)=\dfrac{5}{8}\times \dfrac{3}{8}=\dfrac{15}{64}$$

C)

$$P(WW)=\dfrac{3}{8}\times \dfrac{3}{8}=\dfrac{9}{64}$$

D)

$$P(WB)=\dfrac{3}{8}\times \dfrac{5}{8}=\dfrac{15}{64}$$

E)

$$P(same\ color)=P(BB)+P(WW)$$

$$=\dfrac{25}{64}+\dfrac{9}{64}=\dfrac{17}{32}$$