Question

A shipment of 50 inexpensive digital​ watches, including 10 that are​ defective, is sent to a department store. The receiving department selects 10 at random for testing and rejects the whole shipment if 1 or more in the sample are found defective. What is the probability that the shipment will be​ rejected

Answer 1

Answer: 0.8926

Step-by-step explanation:

Given : A shipment of 50 inexpensive digital​ watches, including 10 that are​ defective.

The probability that a digital​ watch is defective $: p=\dfrac{10}{50}=0.2$

Sample size : n=10

Also, they reject the whole shipment if 1 or more in the sample are found defective.

Using the binomial probability formula :

$P(x)=^nC_xp^x(1-p)^{n-x}$

Let x be the random variable that represents the number of defective watches.

The probability that the shipment will be​ rejected :-

$P(x\geq1)=1-P(0)\\\\=1-^{10}C_0(0.2)^0(0.8)^{10}\\\\=1-(0.8)^{10}=0.8926258176\approx0.8926$

Hence, the probability that the shipment will be​ rejected = 0.8926