3. +-16 points My Notes Ask Your Teache The radio broadcast of AM station KTBC c

Question

3. +-16 points My Notes Ask Your Teache The radio broadcast of AM station KTBC can be heard in the neighboring towns of Waterville and Newport or the total number of radio listeners in Waterville and Newport, 75% live in waterville and 25% live in Newport. Radio station KTBC has 25% of the market in Waterville and 30% of the market in Newport (a) If a random listner in Waterville or Newport is surveyed, what is the probability that the listener wll be tuned in to station KTBC (b) If you know that the listener is indeed listening to station KTBC, what then is the conditional probability that the listener lives in Newport?

Explanation / Answer

a) KTBC has
75% of 25% of the market (in Waterville) and
25% of the other 30% of the market (in Newport).

So its listeners are
0.75 * 0.25 + 0.25 * 0.30 = 0.1875 + 0.075 = 0.2625 = 26.25% of the whole market
and that is the probability a radio listener listens to KTBC.

(b) Looking back at the calculation for part (a), we see that it shows
0.1875 of the whole market listening to KTBC in Waterville and
0.075 of the whole market listening to KTBC in Newport.

So if the listener is listening to KTBC, the probability (conditional on that fact) the listener is in Newport is
0.075 / 0.1875 = 75/18.75  
= about 40%

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