Question

Jorgensens, an Electronics

distributor, just received ashipment of 12 DVDPlayers. Shortly after arrival the
manufacturer called to saythat that he had accidentally shipped
five defective units with theshipment. Mr. Jorgensen immediately
pulled ten of the unitsand tested two of them. What is the
probability that neitherof them was defective?

Answer 1

Answer: 0.3399

Explanation:

The binomial probability distribution formula to find the probability of getting success in x trial:-

`P(x)=^nC_xp^x(1-p)^(n-x)`, where n is the number of trials and p is the probability of getting success in each trial.

Given : Jorgensens received a shipment of 12 DVD Players. Shortly after arrival the manufacturer called to say that that he had accidentally shipped five defective units with the shipment.

i.e. The proportion of the defective units :
`p=(5)/(12)\approx0.417`

Also, Mr. Jorgensen pulled ten of the units and tested two of them.

For n=2, the probability that neither of them was defective:-

`P(x=0)=^(2)C_0(0.417)^0(1-0.417)^(2)\\\\=(1)(1)(0.583)^(2)\ \ \ [\text{ Since}^nC_0=1]\\\\=0.339889\approx0.3399`

Hence, the probability that neither of them was defective = 0.3399