Question

The probability that an electronic device produced by a company does not function properly is equal to 0.1. If 10 devices are bought, then the probability, to the nearest thousandth, that 7 devices function properly is

A. 0.057
B. 0.478
C. 0.001
D. 0

Answer 1

Correct option: A. P=0.057

Explanation:

Binomial Distribution

The binomial distribution fits the case of n independent events each one with a probability of success equal to p where k successes have been achieved.

The PMF (Probability Mass Function) of the binomial distribution is

`\displaystyle P(k,n,p)=\binom{n}{k}p^kq^(n-k)`

Where
`q = 1-p`

The individual probability that an electronic device does not function properly is p=0.1. We know n=10 devices have been bought and we want to compute the probability that 7 devices function properly. Please notice that this is not the value of k since p is the probability of failure. The correct value of k=10-7=3. The required probability is

`\displaystyle P(3,10,0.1)=\binom{10}{3}0.1^30.9^(10-3)`

`\boxed{P=0.057}`