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?

a. 0.9604
b. 0.0392
c. 0.0196
d. 2

Answer 1

The probability that exactly one switch is good out of two switches in a manufacturing plant where 2% of all switches are defective can be calculated using the binomial distribution formula. The answer is 0.0392.

Step-by-step explanation:

To find the probability that exactly one switch is good, we can use the binomial distribution formula. Let's denote a good switch as G and a defective switch as D. The probability of getting a good switch is 1 - 0.02 = 0.98 and the probability of getting a defective switch is 0.02. We want exactly one good switch out of two switches, so we can calculate this probability by multiplying the probability of getting a good switch for one switch and multiplying it by the probability of getting a defective switch for the other switch, and then multiplying by the number of ways we can arrange the switches:

Therefore, the probability that exactly one switch is good is 0.0392 (Option b).