Table of Contents

- 1 What is the probability that it is defective?
- 2 What is the probability that there will be at least one defective?
- 3 What is the probability at least one of the components does not fail?
- 4 What is the probability of getting at least one head?
- 5 How do you find the average number of errors per page?
- 6 What is the average number of typographical errors per page?

## What is the probability that it is defective?

Probability of defect is the statistical chance that a product or process will not meet performance specifications or lie within the defined upper and lower specification limits. It is the ratio of expected defects to the total output.

### What is the probability that there will be at least one defective?

Getting no defective items. 1 – (1/5) =4/5. The probability of getting at least one defective item when drawing three items from a batch of 6 items when 2 items are defective is 4/5 or 80\%.

#### What is the probability at least one of the components does not fail?

(B) The probability that at least one component fails is 1 minus the probability that all succeed. Since the probability of one component succeeding is 1 minus 0.1, or 0.9, the probability that all succeed is (0.9)6 = 0.53, and 1–0.53 = 0.47.

**What is the probability that none of the items has a defect?**

The probability none is defective is (0.94)60, and therefore the probability at least one is defective is 1−(0.94)60.

**What is the probability of at least one event occurring?**

To calculate the probability of an event occurring at least once, it will be the complement of the event never occurring. This means that the probability of the event never occurring and the probability of the event occurring at least once will equal one, or a 100\% chance.

## What is the probability of getting at least one head?

7/8

The probability of getting at least one head is 7/8.

### How do you find the average number of errors per page?

Assuming Poisson law for the number of errors per page, find the probability that a random sample of 5 pages will contain no error. The average number of typographical errors per page in the book is given by λ = (390/520) = 0.75.

#### What is the average number of typographical errors per page?

The average number of typographical errors per page in the book is given by λ = (390/520) = 0.75. The required probability that a random sample of 5 pages will contain no error is given by : [P (X=0)]5 = (e-0.75)5 = e-3.75

**What is the percentage of defective blades in blades?**

One fifth percent of the the blades produced by a blade manufacturing factory turn out to be defective. The blades are supplied in packets of 10. Use Poisson distribution to calculate the approximate number of packets containing no defective, one defective and two defective blades respectively in a consignment of 1,00,000 packets (e–0.2 =.9802)

**How do you find the number of packets with no defective?**

(i) Number of packets containing no defective = N p (o) = 1,00,000 × e–0.02 Example 7.18 If the probability that an individual suffers a bad reaction from injection of a given serum is 0.001, determines the probability that out of 2,000 individuals (a) exactly 3, and (b) more than 2 individuals will suffer a bad reaction.