Question

A box contains 15 transistors, 5 of which are defective. If 5 are selected at random, find the probability that

a. All are defective. ​(Type a fraction. Simplify your​ answer.)
b. None are defective. ​(Type a fraction. Simplify your answer.)

Answer 1

The probability that all 5 selected transistors are defective is 1/3003. The probability that none of the selected transistors are defective is 84/1001.

Step-by-step explanation:

a. To find the probability that all 5 selected transistors are defective, we need to find the probability of selecting a defective transistor at each trial.

The probability of selecting a defective transistor in the first trial is 5/15. Since the selection is done without replacement, the probability of selecting a defective transistor in the second trial is 4/14, and so on. Multiply these probabilities together to find the probability that all 5 selected transistors are defective:

P(all defective) = (5/15) * (4/14) * (3/13) * (2/12) * (1/11) = 120/360360 = 1/3003

b. To find the probability that none of the selected transistors are defective, we need to find the probability of selecting a non-defective transistor at each trial. The probability of selecting a non-defective transistor in the first trial is 10/15. Multiply these probabilities together to find the probability that none of the selected transistors are defective:

P(none defective) = (10/15) * (9/14) * (8/13) * (7/12) * (6/11) = 3024/360360 = 84/1001