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

Answer:

The probability that exactly one switch is good is

$P(x) =0.0392$

Step-by-step explanation:

The probability that a switch is defective is:

$P(D) = \frac{2}{100} =0.02$

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:

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

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

$P(x) =0.0392$

Answer 2

Answer:

P (exactly one good switch) = 0.0392

Step-by-step explanation:

We know that 2% of all switches are defective.

P (defective) = $\frac{2}{100} =0.02$

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) = $(0.02 \times 0.95) + (0.02 \times 0.95)$ = 0.0392