Question

Question 3. (20 pts.) 1. A drawer contains black, brown, and white socks. How many socks ensure two of the same color? 2. With 2,0,3 and 6 how many three digits even numbers can be generated without replacements? 3. We selected 20 persons by the random. What is the probability that only 3 of them have the same birthday at August? Find the probability that only 3 of them have the common month for their birthday?

Answer 1

1.

4 socks ensures 2 of the same color. Let us take the worst scenario here, suppose someone selected 1 sock, it can be any color. Then, selected another, it is some other color as well and in the third selection, it can be the third color. But now we have all the 3 color socks.

Selecting a socks now ensures 2 socks of the same color.

The answer is 4.

2.

A

B

C

Here, for the number to be even, C can take the values of 0, 2 and 6, which are 3. B can take any of the 4 values whereas A can take 2, 3 and 6.

Total numbers = No of values A can take * No of values B can take * No of values C can take

Total numbers = 3*4*3 = 36

3.

The probability of a birthday in a month is 1/12 as there are 12 months.

For 3 persons to have their birthdays in the same month will be (1/12)*(1/12)*(1/12).

Number of ways of selecting 3 persons from 20 = 20C3 = 1140

P = 1140*(1/12)**3 = 1140/1728 = 0.66