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.
The sum of the probabilities of picking a white, black, and yellow pair of socks must equal 1. Let's call the probability of picking a yellow pair of socks "y". Then we can set up the following equation:
start fraction 4 over 9 end fraction + start fraction 7 over 18 end fraction + y = 1
To solve for y, we first need to find a common denominator for the fractions on the left side:
start fraction 8 over 18 end fraction + start fraction 7 over 18 end fraction + y = 1
Combining the first two fractions, we get:
start fraction 15 over 18 end fraction + y = 1
Subtracting 15/18 from both sides, we get:
y = start fraction 3 over 18 end fraction
Simplifying the fraction, we get:
y = start fraction 1 over 6 end fraction
Therefore, the probability of picking a yellow pair of socks is (A) start fraction 1 over 6 end fraction.
To solve this problem, we need to use the fact that the sum of the probabilities of all possible outcomes must be equal to 1.
Let's assign variables to represent the probability of picking a white pair of socks, a black pair of socks, and a yellow pair of socks:
Let W be the probability of picking a white pair of socks.
Let B be the probability of picking a black pair of socks.
Let Y be the probability of picking a yellow pair of socks.
We are given:
W = 4/9 (probability of picking a white pair of socks)
B = 7/18 (probability of picking a black pair of socks)
To find Y (probability of picking a yellow pair of socks), we can use the fact that the sum of the probabilities of all possible outcomes must be equal to 1. Therefore:
W + B + Y = 1
Substituting the given values:
4/9 + 7/18 + Y = 1
First, let's simplify the fractions:
4/9 = 8/18
Substituting:
8/18 + 7/18 + Y = 1
Combining like terms:
15/18 + Y = 1
To isolate Y, subtract 15/18 from both sides of the equation:
Y = 1 - 15/18
To simplify the expression on the right-hand side:
Y = 3/18
Reducing the fraction:
Y = 1/6
Therefore, the probability of picking a yellow pair of socks is 1/6.
So, the answer is A. Start Fraction 1 over 6 End Fraction.