Question

In your sock drawer you have 6 blue, 7 gray, and 2 black socks. Half asleep one morning you grab 2 socks at random and put them on.
1. Find the probability you end up wearing the following socks. (Round your answers to four decimal places.)
a) 2 blue socks.
b) no gray socks.
c) at least 1 black sock.
d) matching socks.

Answer 1

Answer:

a) 0.1429

b) 0.2667

c) 0.3067

d) 0.3524

Step-by-step explanation:

Blue = 6

Gray = 7

Black = 2

Number of socks = 15

a) 2 blue socks.

The probability of getting two consecutive blue socks is:

$P(Blue=2) = \frac{6}{15}*\frac{5}{14}=0.1429$

b) no gray socks.

The probability of getting no grey socks with two picks is:

$P(G=0) = \frac{15-7}{15} *\frac{14-7}{14}=0.2667$

c) at least 1 black sock.

The probability of getting at least one black sock is:

$P(B>0) = 1 - P(B=0)\\P(B>0) =1 - (\frac{13}{15}*\frac{12}{15})\\P(B>0) = 0.3067$

d) matching socks.

The probability of getting matching socks is the sum of the probabilities of getting 2 black, 2 blue or 2 gray socks:

$P(matching) = P(Blue=2)+P(Black=2)+P(G)\\P(matching) =\frac{6}{15}* \frac{5}{14} +\frac{2}{15}* \frac{1}{14}+\frac{7}{15}* \frac{6}{14} \\P(matching) = 0.3524$