Question

device uses five silicon chips. Suppose the five chips are chosen at random from a batch of a hundred chips out of which five are defective. What is the probability that the de\"ice contains no defecth'e chip when it is made up from one batch?

Answer 1

Answer:

76.96% probability of no defective chips.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The combinations formula is important to solve this question.

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

Desired outcomes:

Sample of 100 chips, of which 5 are defective and 100-5 = 95 are not defective.

We want to find the probability that there are no defective chips.

So this is a combination of 5 from a set of 95.

$D = C_{95,5} = \frac{95!}{5!(95-5)!} = 57940519$

Total outcomes:

Combination of 5 from a set of 100.

$T = C_{100,5} = \frac{100!}{5!(100-5)!} = 75287520$

Probability:

$P = \frac{D}{T} = \frac{57940519}{75287520} = 0.7696$

76.96% probability of no defective chips.