Question

The radio broadcast of AM station KTBC can be heard in the neighboring towns of Waterville and Newport. Of the total number of radio listeners in Waterville and Newport, 75% live in Waterville and 25% live in Newport. Radio station KTBC has 20% of the market in Waterville and 30% of the market in Newport.
If a random listener in Waterville or Newport is surveyed, what is the probability that the listener will be tuned in to station KTBC?

Answer 1

Answer: The required probability is 22.5%.

Step-by-step explanation:

Since we have given that

Probability of radio listeners live in Waterville = 0.75

Probability of radio listeners live in Newport = 0.25

Probability of radio station KTBC in Waterville = 0.20

Probability of radio station KTBC in Newport = 0.30

So, using "Multiplication rule of Probability":

Probability that the listener will be tuned in to station KTBC is given by

$0.75\times 0.20+0.25\times 0.30\\\\=0.15+0.075\\\\=0.225\\\\=22.5\%$

Hence, the required probability is 22.5%.