Math, asked by hridya81, 5 months ago

From the production process which turns 5% defective on an average,a sample size 10 is drawn. Find the probability that the sample contains i).no defective ii). at most one defective iii).atleast one defective​

Answers

Answered by amitnrw
3

Given : From the production process which turns 5% defective on an average, a sample of size 10 is drawn.

To Find : the probability that the sample contains

i) no defective;

ii) at most one defective;

iii) atleast one defective.?

Solution:

turns 5% defective

Probability of defective p = 0.05

probability of non defective  q  = 1  -0.05 = 0.95

sample size  n  = 10

P(x)  = ⁿCₓpˣqⁿ⁻ˣ

i) no defective => x = 0

P(0) = ¹⁰C₀(0.05)⁰(0.95)¹⁰  = (0.95)¹⁰  = 0.5987

at most one defective;

= P(0) + P(1)

= ¹⁰C₀(0.05)⁰(0.95)¹⁰  + ¹⁰C₁(0.05)¹(0.95)⁹

=  (0.95)¹⁰ + 0.5(0.95)⁹

= (0.95)⁹ (0.95  + 0.5)

= (0.95)⁹ (1.45)

= 0.91386

atleast one defective

= 1 - P(0)

= 1 -   0.5987

= 0.4013

learn More:

If probability is 0.55 that a person will believe in a piece of fake news ...

https://brainly.in/question/19591686

A die is rolled eight times and a 2, 3, 5 and 6 is considered a ...

https://brainly.in/question/20879616

The probability of a component's failure is 0.05. Out of 14 ...

https://brainly.in/question/19727623

Similar questions