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
b. None are defective

Answer 1

The probability of selecting all defective transistors is (5/15)^5, and the probability of selecting none defective transistors is (10/15)^5.

Step-by-step explanation:

To find the probability that all 5 selected transistors are defective, we need to calculate the probability of selecting a defective transistor and multiply it by itself 5 times. Since there are 5 defective transistors out of a total of 15, the probability of selecting a defective transistor is 5/15. So, the probability of selecting all 5 defective transistors is (5/15) * (5/15) * (5/15) * (5/15) * (5/15).

To find the probability that none of the selected transistors are defective, we need to calculate the probability of selecting a non-defective transistor and multiply it by itself 5 times. Since there are 10 non-defective transistors out of a total of 15, the probability of selecting a non-defective transistor is 10/15. So, the probability of selecting none of the transistors to be defective is (10/15) * (10/15) * (10/15) * (10/15) * (10/15).