Question

Among 9 electrical components exactly one is known not to function properly. if 4 components are randomly selected, find the probability that at least one does not function properly.

Answer 1

The probability is 0.44444.

Explanation:

Among 9 electrical components exactly one is known not to function properly.

This means 8 components work properly.

If 4 components are randomly selected, the probability that at least one does not function properly is :

`(8c3 *1c1)/(9c4)`

=
`(56)/(126) =0.44444`

Answer: The probability is 0.44444.

Answer 2

0.4444

Explanation:

Use the following property to ease the calculation:

P(At least one)=1-P(None)

Total number of electrical components: 9

Number that does not function well :1

Number that functions well : 8

We have
`^8C_4=70` ways to to choose 4 good components from 8.

We have
`^9C_4=126` ways to choose 4 components from a total of 9.

If all function properly then none is bad, we
`^1C_0=1` way to do this.

P(At least one)=
`1-(^8C_4*^1C_0)/(^9C_4)`

P(At least one)=
`1-(70*1)/(126)`

P(At least one)=0.4444