Question

Suppose that Stephen is the quality control supervisor for a food distribution company. A shipment containing many thousands of apples has just arrived. Unknown to Stephen, 11% of the apples are damaged due to bruising, worms, or other defects. If Stephen samples 10 apples from the shipment, use the binomial distribution to estimate the probability that his sample will contain at least one damaged apple.

Answer 1

Answer: 0.6881828007

Step-by-step explanation:

Given : The probability of the apples are damaged due to bruising, worms, or other defects : p= 0.11

The sample size : n= 10

Let x be the number of  apples are damaged due to bruising, worms, or other defects in the sample.

Using binomial probability formula : $P(x)=^nC_xp^x(1-p)^{n-x}$

The probability that his sample will contain at least one damaged apple will be :-

$P(x\geq1)=1-P(x=0)\\\\=1-(^{10}C_0(0.11)^0(1-0.11)^{10})\\\\=1-(1)(0.89)^{10}\\\\=1-0.3118171993\\\\=0.6881828007$