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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
12
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B
27
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C
1249
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D
43175
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Solution

## The correct option is B 27For 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 Monday1. 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- 27

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