Question

Choose a number $n$ uniformly at random from the set $\{1,2,....,100\}$. Choose one of the first seven days of the year $2014$ at random and consider $n$ consecutive days among the chosen $n$ days.

What is the probability that among the chosen $n$ days, either a Monday or Sunday will be chosen?

• A. $\frac{1}{2}$
• B. $\frac{2}{7}$
• C. $\frac{12}{49}$
• D. $\frac{43}{175}$

Answer 1

The correct option is B $\frac{2}{7}$

For any value of n, if days are chosen consecutively, then out of 7 cases of 7 different cases, there will be only 2 cases when either of monday or sunday will be included.

For example:

n=5, Day chosen is Monday

1. M-T-W-T-F (favoruable case)

2. T-W-T-F-S (unfavourable case)

3. W-T-F-S-S (favourable)

4. T-F-S-S-M (unfavourable case)

5. F-S-S-M-T ( unfavourable)

6. S-S-M-T-W (unfavourable)

7. S-M-T-W-T (unfavourable)

Probability- $\frac{2}{7}$