Question

A drawer has 9 pairs of white socks 7 pairs of black socks 6 pairs of brown socks and 3 pairs of blue socks you get dressed each morning in the dark in randomly reach into the sock drawer to get your socks after a day of wearing the socks you do not replace them until the weekend after you have done some laundry what is the probability that your sock selection goes in the following order for this week?

P(Black then white then white the brown then blue)=____

Answer 1

567/398475 in fraction or 0.0014229249 in decimal

Explanation:

In the question, we are given these values

Total pair of socks = 25 pairs of socks

9 pairs of white socks

7 pairs of black socks

6 pairs of brown socks

3 pairs of blue socks

From the question, we can see that, this is probability without replacement.

Hence,

P(Black then white then white the brown then blue)=

7/25 × 9/24× 8/23 ×6/22 × 3/21

= 9072/6375600

= 567/398475

Therefore, the Probability of picking a Black socks then white socks then white socks , then brown socks and then blue socks = 567/398475 in fraction or 0.0014229249 in decimal

Answer 2

0.0014 = 0.14%

Explanation:

First we need to find the total number of pairs:

9 + 7 + 6 + 3 = 25 pairs

Then, we need to find the probability for each case:

First socks black: 7 pairs over 25: P1 = 7/25

Second socks white: 9 pairs over 24: P1 = 9/24 = 3/8

Third socks white: 8 pairs over 23: P1 = 8/23

Fourth socks brown: 6 pairs over 22: P1 = 6/22 = 3/11

Fifth socks blue: 3 pairs over 21: P1 = 3/21 = 1/7

The final probability will the the product of all probabilities above:

P = (7/25) * (3/8) * (8/23) * (3/11) * (1/7) = 0.0014 = 0.14%