Company A produces 10% defective products, Company B produces 20% defective products and C produces 5% defective products. If choosing a company is an equally likely event, then find the probability that the product chosen is defective.
Answers
Answer:
35% defective product ans
Given: Percentage of defecctive products company A produces = 10%.
Percentage of defecctive products company B produces = 20%.
Percentage of defecctive products company C produces = 5%.
To find: The probability that the product chosen is defective
Solution: Let the event of selecting a particular company be P(E).
As such, P(E) = 1/3 since there are 3 companies.
And let the event of choosing a defective product be P(A).
Now the probability of choosing a defective product produced by A
= P(E) × P(A|E)
= (1/3) × (10/100)
Similarly, the probability of choosing a defective product produced by B
= P(E) × P(B|E)
= (1/3) × (20/100)
The probability of choosing a defective product produced by C
= P(E) × P(C|E)
= (1/3) × (5/100)
Therefore, the required probability that the product chosen is defective = P(A)
= (1/3) × (10/100) + (1/3) × (20/100) + (1/3) × (5/100)
= (10 + 20 + 5)/300
= 35/300
= 0.1167
= 0.12
Answer: 0.12