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+2 votes

Seven (distinct) car accidents occurred in a week. What is the probability that they all occurred on the same day?

  1. $\frac{1}{7^7}$
  2. $\frac{1}{7^6}$
  3. $\frac{1}{2^7}$
  4. $\frac{7}{2^7}$
asked in Probability by Veteran (58.2k points)   | 803 views

2 Answers

+10 votes
Best answer

answer - B [EDIT]

for every car accident we can pick a day in 7 ways

total number of ways in which accidents can be assigned to days = 77

probability of accidents happening on a particular day = 1/77

we can choose a day in 7 ways

hence probability = 7/77= 1/76


answered by Boss (9.2k points)  
selected by

the answer is B. The number of ways you can choose the "same day" is 7. The probability of all the accidents happening on same day is 1/77 . So 7*(1/77) is 1/76.

i missed that i'll edit the answer
We can solve this problem using poisson distribution... answer is 8*10^-6 which is nearly match to the option (B).

Am i right? @ankit
+6 votes

P(accident on a single day out of 7 days)=$\frac{1}{7}$

P(all accident occurred on the same day Out of 7 Day)= $\binom{7}{1}$ $(\frac{1}{7})^{7}$ $(\frac{6}{7})^{0}$   = $\frac{7}{7^{7}}$ = $\frac{1}{7^{6}}$  //Binomial Distribution So Option B is Correct Ans

(Means selecting single day out of 7 days and all the 7 accident should happen on same day with probability $\frac{1}{7}$)

answered by Veteran (16.3k points)  
edited by

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