GATE CSE
First time here? Checkout the FAQ!
x
+2 votes
900 views

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 (58.9k points)   | 900 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 (16.8k points)  
edited by


Top Users May 2017
  1. akash.dinkar12

    3568 Points

  2. pawan kumarln

    2206 Points

  3. Bikram

    1940 Points

  4. sh!va

    1682 Points

  5. Arjun

    1650 Points

  6. Devshree Dubey

    1272 Points

  7. Debashish Deka

    1270 Points

  8. Angkit

    1056 Points

  9. LeenSharma

    1028 Points

  10. Arnab Bhadra

    904 Points

Monthly Topper: Rs. 500 gift card
Top Users 2017 May 22 - 28
  1. Bikram

    1026 Points

  2. pawan kumarln

    832 Points

  3. Arnab Bhadra

    818 Points

  4. akash.dinkar12

    448 Points

  5. Arjun

    378 Points


22,897 questions
29,213 answers
65,339 comments
27,714 users