Question

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

• A. $\frac{1}{7^7}$
• B. $\frac{1}{7^6}$
• C. $\frac{1}{2^7}$
• D. $\frac{2}{2^7}$

Answer 1

The correct option is B $\frac{1}{7^6}$

Probability of occuring 1 car accident in a week = 1/7

Probability of occuring 7 car accident in a week
$=\frac{1}{7}\times \frac{1}{7}\times \frac{1}{7}\times \frac{1}{7}\times \frac{1}{7}\times \frac{1}{7}\times \frac{1}{7}={\left(\frac{1}{7}\right)}^7$

Favourable ways for "all occur on a same day"=$7\times 1\times 1\times 1\times 1\times 1\times 1=7$

So required probability $=\frac{fav}{total}=\frac{7}{7^7}=\frac{1}{7^6}$