Question

1. A box contains 85 good and 15 defective screws. If 10 screws are used, what is the probability that none is defective?

2. If n balls are placed at random into n cells, find the probability that exactly one cell remains empty.

Answer 1

1.

Let the number of defectives be X. Given that in a box of 100 screws, 15 are defective. The probability of obtaining a defective is p = 0.15

So X follows binomial distribution with parameters n=10, p=0.15

Here we are to obtain P(X=0)

2.

n balls can be distributed among n cells in nⁿ equally likely ways.

The empty cell can be chosen in n ways. For each such choice, the cell that will have 2 balls can be chosen in (n-1) ways.

For each such choice, the two balls that enter in the above mentioned cell can be chosen in ways. There are (n-2) remaining cells and (n-2) remaining balls. So the remaining balls can be distributed in the remaining cells in (n-2)! ways

So the required probability is

Hopefully this will help you. In case of any query, do comment. If you are satisfied withthe answer, give it a like. Thanks.