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

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

(A) $\dfrac{1}{7^7}$,    (B) $\dfrac{1}{7^6}$,    (C) $\dfrac{1}{2^7}$,    (D) $\dfrac{7}{2^7}$ 

(GATE 2001) 

Answer: (B) $\dfrac{1}{7^6}$ 

Explanation: 

The probability that all accidents occurred on Monday $= \dfrac{1}{7^7}$ 

The probability that all accidents occurred on Tuesday $= \dfrac{1}{7^7}$ 

$\cdots$    $\cdots$    $\cdots$    $\cdots$    $\cdots$    $\cdots$

$\cdots$    $\cdots$    $\cdots$    $\cdots$    $\cdots$    $\cdots$

The probability that all accidents occurred on Sunday $= \dfrac{1}{7^7}$ 

Therefore, the probability that they all occurred on the same day is 

$7 \times \dfrac{1}{7^7} = \dfrac{1}{7^6}$.