JEE Main 2026 Jan 24 Shift 1, Mathematics Q17: Binomial Trials And Binomial Distribution

Each draw is independent (with replacement) with $P(\text{defective})=\frac{1}{10}$ and $P(\text{non-defective})=\frac{9}{10}$.

Using binomial probabilities for $n=8$:

$P(\text{exactly 7 defective})=\left(\genfrac{}{}{0ex}{}{8}{7}\right){\left(\frac{1}{10}\right)}^7\left(\frac{9}{10}\right)=\frac{72}{10^8}$.

$P(\text{exactly 8 defective})={\left(\frac{1}{10}\right)}^8=\frac{1}{10^8}$.

$P(\text{at least 7})=\frac{72+1}{10^8}=\frac{73}{10^8}$.