Question

Seven chits are numbered $1$ to $7$. Three are drawn one by one with replacement. The probability that the least number on any selected chit is $5$ is

• A. $1-{\left(\frac{2}{7}\right)}^4$
• B. $4{\left(\frac{2}{7}\right)}^4$
• C. ${\left(\frac{3}{7}\right)}^3$
• D. None of these

Answer 1

The correct option is C

${\left(\frac{3}{7}\right)}^3$

Explanation for the correct answer:

Finding the probability that the chit contains $5,6,or7$:

Total number of chits $=7$

The event that the least number on any selected chit is $5$is $\{5,6,7\}$

So, the probability of $5$ or $6$ or $7$ in one draw $=\frac{3}{7}$

Therefore, in each of $3$ draws, the probability that the chit contains $5,6,or7$ is ${\left(\frac{3}{7}\right)}^3$.

Therefore, option (C) is correct.