In a local cellular phone area,company A accounts for 60% of the cellular phone market,while company B accounts for the remaining 40% of the market.Of the cellular calls made with company A,1% of the calls will have some sort of interference,while 2% of the cellular calls with company B will have interference.If a cellular call is selected at random,the probability that it will not have interference is
A)0.014
B)0.028
C)0.14
D)0.986

Question

Quizplus · Accepted Answer

We can use the Law of Total Probability to calculate the probability that a randomly selected cellular call does not have interference.

Let A be the event that the call is made with company A, and let B be the event that the call is made with company B. Then we have:

P(no interference) = P(no interference | A)P(A) + P(no interference | B)P(B)

= (1-0.01)(0.6) + (1-0.02)(0.4)

= 0.59 + 0.38

= 0.97

Therefore, the probability that a randomly selected cellular call does not have interference is 0.97 or 0.986 in decimal form.

The closest answer choice is D, which is 0.986.

In a Local Cellular Phone Area,company a Accounts for 60