Question

question: in a shipment of toys from a manufacturer, the probability that a toy is defective is $\frac{1}{50}$. if marie selects 2 toys from a shipment, what is the probability that both toys are defective? $\frac{1}{25}$ $\frac{1}{50}$ $\frac{1}{100}$ $\frac{1}{2,500}$

Explanation:

Step1: Identify probability of first toy being defective

The probability that a single - toy is defective is $p_1=\frac{1}{50}$.

Step2: Identify probability of second toy being defective

Assuming the selection of toys is independent, the probability that the second toy is defective is also $p_2 = \frac{1}{50}$.

Step3: Use multiplication rule for independent events

For two independent events $A$ and $B$, the probability that both $A$ and $B$ occur is $P(A\cap B)=P(A)\times P(B)$. Here, the probability that both toys are defective is $P = \frac{1}{50}\times\frac{1}{50}=\frac{1}{2500}$.

Answer:

$\frac{1}{2500}$