Suppose you have a drawer full of white, black, and yellow pairs of socks. If the probability of picking a white pair of socks is 4/9, in the probability of picking a black pair of socks is 7/18, what is the probability of picking a yellow pair of socks?
A. 1/6
B. 5/12
C. 7/15
D. 16/27
The sum of the probabilities of picking a white, black, or yellow pair of socks must be 1. Therefore, we can first find the probability of picking a white or black pair of socks and subtract it from 1 to get the probability of picking a yellow pair of socks.
The probability of picking a white or black pair of socks is:
4/9 (probability of white) + 7/18 (probability of black)
To add these fractions, we need a common denominator. The least common multiple of 9 and 18 is 18, so we can rewrite the fractions as:
8/18 (4/9 as equivalent fraction with denominator 18) + 7/18
Adding these fractions gives us:
15/18
Simplifying this fraction (dividing both numerator and denominator by 3) gives:
5/6
Therefore, the probability of picking a yellow pair of socks is:
1 - 5/6 = 1/6
So the answer is A. 1/6.