Question

At a manufacturing plant where switches are made, it is a known fact that 2% of all switches are defective. If two switches are used in a device, what is the probability that exactly one switch is good?

Answer 1

P (exactly one good switch) = 0.0392

Explanation:

We know that 2% of all switches are defective.

P (defective) =
`(2)/(100) =0.02`

So P (not defective) = 1 - P (defective) =
`1-0.02=0.98`

Now we have to find the probability of one good switch out of 2 that are used in a device.

P (exactly one good switch) =
`(0.02 * 0.95) + (0.02 * 0.95)` = 0.0392

Answer 2

The probability that exactly one switch is good is

`P(x) =0.0392`

Explanation:

The probability that a switch is defective is:

`P(D) = (2)/(100) =0.02`

The probability that a switch is not defective is

`P(D') = 1-P(D)=0.98`

Therefore, if two switches are selected, the probability that exactly 1 is good is:

`P(1=1)=P (D) P (D ') + P (D') P (D)`

`P(x)=(0.02)(0.98) + (0.98)(0.02)`

`P(x) =0.0392`