Question

Suppose your top drawer contains different colored socks: 12 are white, 16 are black, 8 are pink, and 10 are blue. All socks in the drawer are loose (unpaired). In the morning, you randomly select two socks, one at a time. Calculate the following probabilities, writing your answer either as a decimal or a fraction.

(d) What is the probability that you get one black sock and one white sock?

Answer 1

Answer:

δ = 0.1855...

Step-by-step explanation:

12 are white, 16 are black, 8 are pink, and 10 are blue, there are 46 socks.

To select  2 random socks we have the probability of Ω.

Lets say that the possibility to pick one black is α and the possibility to pick one white is β.

Our final solution is δ = (α·β)/Ω, where δ represents probability to get one black and one white sock out of all 46 socks.

Ok so for finding α, β and Ω we use the equation called Binomial coefficient,  presented in a photo.

Lets look at Ω. For choosing 2 random socks out of 46 we use formula form the photo, where n = 46 and k = 2 ---> Ω = $\frac{46!}{2!*(46-2)!}$ ---->  Ω = 1035

• Now for α we say that n = 16 and k = 1 ---> α = 16
• Using same principle for white, we have n = 12, k = 1 ---> β = 12

δ = (α·β) / Ω ---> δ = 192/1035 ---> δ = 0.1855...