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Seven (distinct) car accidents occurred in a week. What is the probability that they all occurred on the same day?
- a)1/77
- b)1/76
- c)1/27
- d)7/27
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Seven (distinct) car accidents occurred in a week. What is the probabi...
Sample space = 77
All accidents on the same day = 7 ways (all on Monday, all on Tuesday...)
So, required probability
All accidents on the same day = 7 ways (all on Monday, all on Tuesday...)
So, required probability
Most Upvoted Answer
Seven (distinct) car accidents occurred in a week. What is the probabi...
Solution:
We have to find the probability that all seven accidents occurred on the same day.
Total number of ways to distribute seven accidents over seven days = 7^7 (each accident can happen on any of the seven days).
Number of ways to distribute seven accidents over any six days = 6*7^6 (choose any one of the six days to have two accidents, then distribute the remaining five accidents over the remaining six days).
Therefore, the probability that all seven accidents occurred on the same day is given by:
P(all on same day) = (7^7 - 6*7^6)/7^7 = 1/76
Hence, the correct option is (b) 1/76.
We have to find the probability that all seven accidents occurred on the same day.
Total number of ways to distribute seven accidents over seven days = 7^7 (each accident can happen on any of the seven days).
Number of ways to distribute seven accidents over any six days = 6*7^6 (choose any one of the six days to have two accidents, then distribute the remaining five accidents over the remaining six days).
Therefore, the probability that all seven accidents occurred on the same day is given by:
P(all on same day) = (7^7 - 6*7^6)/7^7 = 1/76
Hence, the correct option is (b) 1/76.
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