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 and the probability of picking a black pair of socks is 7/18 what is the probability of picking a yellow pear of socks?
Since there are only three colors of socks, the sum of the probabilities of picking a white, black, or yellow pair of socks is equal to 1. Therefore, we can find the probability of picking a yellow pair of socks by subtracting the sum of the probabilities of picking a white or black pair of socks from 1:
1 - (4/9 + 7/18) = 1 - 8/18 = 10/18 = 5/9
So the probability of picking a yellow pair of socks is 5/9.
To find the probability of picking a yellow pair of socks, we can use the fact that the sum of the probabilities of all possible outcomes must equal 1.
Let's break down the problem step-by-step:
1. Let W, B, and Y represent the events of picking a white, black, and yellow pair of socks, respectively.
2. We are given the probabilities of picking a white pair of socks (P(W) = 4/9) and picking a black pair of socks (P(B) = 7/18).
3. The probability of picking a yellow pair of socks (P(Y)) can be found by subtracting the sum of probabilities of picking white and black pairs of socks from 1.
P(Y) = 1 - P(W) - P(B)
P(Y) = 1 - (4/9) - (7/18)
4. To simplify the calculation, we need to find a common denominator for (4/9) and (7/18).
The least common multiple of 9 and 18 is 18.
P(Y) = 1 - (8/18) - (7/18)
5. Combine the fractions with a common denominator.
P(Y) = 1 - (8 + 7)/18
P(Y) = 1 - 15/18
6. Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 3.
P(Y) = 1 - (5/6)
7. Further simplify the expression to get the final probability.
P(Y) = (6/6) - (5/6)
P(Y) = 1/6
Therefore, the probability of picking a yellow pair of socks is 1/6.
To find the probability of picking a yellow pair of socks, we can use the fact that the sum of probabilities of all possible outcomes must equal 1.
Let's denote the probability of picking a yellow pair of socks as P(Yellow).
Given that the probability of picking a white pair of socks is 4/9 and the probability of picking a black pair of socks is 7/18, we can write the equation:
P(White) + P(Black) + P(Yellow) = 1
We are given that P(White) = 4/9 and P(Black) = 7/18. Plugging these values into the equation:
4/9 + 7/18 + P(Yellow) = 1
To solve for P(Yellow), we can simplify the equation:
8/18 + 7/18 + P(Yellow) = 1
15/18 + P(Yellow) = 1
Now, we can isolate P(Yellow) by subtracting 15/18 from both sides of the equation:
P(Yellow) = 1 - 15/18
P(Yellow) = 3/18
Simplifying this fraction, we get:
P(Yellow) = 1/6
Therefore, the probability of picking a yellow pair of socks is 1/6.