Question

More defective components: A lot of 1060 components contains 229 that are defective. Two components are drawn at random and tested. Let A be the event that the first component drawn is defective, and let B be the event that the second component drawn is defective. Write your answer as a fraction or a decimal, rounded to four decimal places.?Explain.

Answer 1

Required Probability = 0.0467

Explanation:

We are given that a lot of 1060 components contains 229 that are defective.

Two components are drawn at random and tested.

A = event that the first component drawn is defective

B = event that the second component drawn is defective

So,P(first component drawn is defective,A)=(No. of defective component)÷

(Total components)

P(A) = 229/1060

Similarly, P(second component drawn is defective,A) = 229/1060

Therefore, P(both component drawn defective) =
`(229)/(1060) * (229)/(1060)` = 0.0467 .

Answer 2

The probability of event A is 0.2160.

The probability of event B is 0.2153.

Explanation:

Assume that the random variable X is defined as the number of defective components in a lot.

It is provided that of the 1060 component 229 are defective.

The probability of selecting a defective component is:

`P(X)=(229)/(1060)=0.2160`

The proportion of defective components in a lot of 1060 is 0.2160.

It is provided that two components are selected to be tested.

Assuming the selection were without replacement.

A = the first component drawn is defective

B = the second component drawn is defective

• Compute the probability of event A:

The probability of selecting a defective component from the entire lot

of 1060 component is 0.2160.

Thus, the probability of event A is 0.2160.

• Compute the probability of event B:

According to event A, the first component selected was defective.

So now there are 228 defective components among 1059

components.

`P(B)=(228)/(1059)= 0.2153`

Thus, the probability of event B is 0.2153.

Both the probabilities are almost same.

This implies that the probability of selecting a defective component from the entire population of these components is approximately 0.2160.