Hepl A batch of 150 toy cars contains 10 toy cars that are defective. Two are se

Question

Hepl

A batch of 150 toy cars contains 10 toy cars that are defective. Two are selected at random from the batch without replacement.

a. What is the probability that the first car selected is non-defective?

b. What is the probability that the first car selected is defective?

c. What is the probability that the second car is defective given that the first car was found defective?

d. What is the probability that the second car is defective given that the first car was found non-defective?

e. If the first car is defective and reintroduced in the batch (still as a defective car), would the probability that the second car is found defective change compared to part c? Demonstrate mathematically.

Explanation / Answer

probability that a car is defective = 10/150 = 0.0667

probability that a car is non defective = 1 - 0.0667 = 0.9333

(A)

Probability that the first car is non-defective = 140/150 * (10/149 + 139/149) = 0.9333

(B)

Probability that the first car is defective = 10/150 * (9/149 + 140/149) = 0.0667

(C)

Probability that second car is defective given that the first car was found defective = 9/149 = 0.0604

(D)

Probability that second car is defective given that the first car was found non-defective = 10/149 = 0.0671

(E)

Required probability with replacement = 10/150 = 0.0667

Here the probability is different from the part (C). This is due to replacement.

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