Question

In a box containing $15$ identical bulbs, $5$ are defective. If $5$ bulbs are drawn at random from the box with replacement. The probability that atleast one of them is defective is?

• A. $\frac{32}{343}$
• B. $\frac{211}{243}$
• C. $\frac{80}{243}$
• D. $\frac{32}{243}$

Answer 1

The correct option is B $\frac{211}{243}$

Probability that at least one is defective=1-Probability that no one is defective

Probability that no one is defective=$({\frac{10}{15})}^5=32/243$

Probability that at least one is defective=1-32/243=211/243