Question

There are 20 total socks, 10 white and 10 black. This makes 10 total matching pairs of 5 pair of white and 5 pair of black.

6. What is the total probability of picking a white sock and then another white sock (one pair of white socks)?

7. What is the probability of picking either a pair of white socks or a pair of black socks?

8. If each time you pick a sock from the drawer a sock just like it magically replaces it, what is the probability of picking either a pair of white socks or a pair of black socks?

9. How can you guarantee success of picking a matching pair? In other words, what is the minimum number of socks needing to be picked to guarantee a matching pair? (Hint: There is a right answer to this question!)

10. Explain dependent and independent trials and then further describe the difference between Question 7 and Question 8 as it relates to dependent and independent trials.

Answer 1

6)

Probability of picking a pair = (10/20)*(9/19) = 9/38

7)

Either a black pair or a white pair in the first two picks = sum of white pair+sum of black pair = 9/38 + 9/38 = 9/19

8)

If after picking the socks are magically replaced, that means the total number of white and black socks remain constant even after the picking
= (10/20)*(10/20) + (10/20)*(10/20) = 1/2

9)

if all the socks are either white or black, you need to pick (no of colours)+1 socks to get at least one matched pair.

here 3 socks

10)

Dependent trails are the trails where the outcome of the previous event will have an impact on the outcome of the next trial. As in the Question no. 7, when we pick a white in the first trial, the number of white socks decreases along with the total and the probability of picking a white again, slightly decreases (from 0.5 to 9/19)
In the case of Independent trials (like a flip of coin), outcome of the previous trail will not affect the outcome of the current trail. When the socks are magically replaced after each picking, the probability of white in the second trial remained the same.