Question

In your top dresser drawer are 6 blue socks and 10 grey socks, unpaired and mixed up. One dark morning you pull two socks from the drawer (without replacement, of course!) What is the probability that the two socks match?A. 0.075
B. 0.375
C. 0.450
D. 0.500

Answer 1

Answer:

D) 0.500

Step-by-step explanation:

Blue Socks = 6

Grey socks = 10

Probabilities to find :

Since there are a total of 16 socks, the probability of both socks being blue is  

Probability(blue) = $(\frac{6}{16} ) \frac{5}{15} =\frac{30}{240} =\frac{1}{8}$

The probability of both being grey is  

Probability(grey)  =$(\frac{10}{16} ) \frac{9}{15} =\frac{90}{240} =\frac{3}{8}$

(Note: After 1 sock is picked , next sock drawn would have a different probability as 1 sock is already picked so it would be 1 minus the total socks available of that color)

The probability two socks match:

Probability(blue) + Probability(grey) = $\frac{1}{8}$ + $\frac{3}{8}$  = $\frac{4}{8}$  =$\frac{1}{2}$ = 0.500