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 four-ninths, and the probability of picking a black pair of socks is
start fraction 7 over 18 end fraction, what is the probability of picking a yellow pair of socks?
A. start fraction 1 over 6 end fraction
B. Start Fraction 5 over 12 End Fraction
C. Start Fraction 7 over 15 End Fraction
D. Start Fraction 16 over 27 End Fraction
Since there are only three colors of socks, the probabilities of picking each color must add up to 1. Therefore, the probability of picking a yellow pair of socks is:
1 - (4/9) - (7/18) = 1/6
So the answer is (A) start fraction 1 over 6 end fraction.
To find the probability of picking a yellow pair of socks, we need to subtract the probabilities of picking white and black pairs of socks from 1 since there are only three colors of socks in the drawer.
Let's denote the probability of picking a yellow pair of socks as P(yellow).
Given:
P(white) = 4/9
P(black) = 7/18
To find P(yellow), we subtract the probabilities of picking white and black socks from 1:
P(yellow) = 1 - P(white) - P(black)
= 1 - 4/9 - 7/18
To simplify the expression, we need to find a common denominator:
P(yellow) = 1 - (4/9) - (7/18)
= 1 - (8/18) - (7/18)
= 1 - (15/18)
= 1 - 5/6
= 1/6
Therefore, the probability of picking a yellow pair of socks is 1/6.
So, the correct answer is:
A. Start Fraction 1 over 6 End Fraction