Question

In a bank, there are 15 coin vending machines: out of 15 machines 5 are defective 3 machines are chosen at random in the bank find the probability that at least one of these is defective? indiabix

Answer 1

There are in all 15 machines.

So total ways to chose 3 machines out of 15 machines = 15C3 = 455

Now 5 machines out of 15 machines are defective.

So 10 machines are non defective.

For at least one to be defective, let us assume none of them is defective.

For choosing all 3 non defective machines there are 10C3 ways = 120 ways.

So number of ways to chose atleast one defective machine are = 455-120 = 335 ways

Probability of choosing at least one defective machine = $\frac{355}{455} =\frac{71}{91} = 0.78$

The probability that at least one of these is defective is 0.78.