Ten percent of Screws produced in a certain factory turnout
to be defective. Find the probability that in a sample of
10 screws chosen at random, exactly two will be
defective.
Answers
Given:
Percentage of screws defected = 10%
Total screws in a box = 100
To find:
The probability that there will be 2 defective screws in a sample of 10 screws.
Solution:
Number of defected items = 10% of 10 = 10/100 * 10 = 1
Probability of getting defected screws =No. of Defected screws/ total screws .
= 1/10 = 0.1
Probability of non defected screws = 1 - Probability of getting defected screws
= 1-0.1 = 0.9
For 2 defected screws:
By binomial distribution method:
We know that P(r) = ⁿCr p^r * (1-p)^(n-r)
Where n is the total number of events,
r is the number of successful events ,
p is the probability of successful events ,
(1-p) is the probability of unsuccessful events.
Probability of 2 defected screws = P(1) = ¹⁰C₂(0.1)² (1- 0.1)⁸
= ¹⁰C₂ (0.1)² (0.9)⁸
P(1) = 0.19371
Probability of exactly two defective screws will be 0.19371.