A car company created a 90-second commercial and purchased enough air time for it to be played at 4 random times during prime time hours of 8 p.m. to 11 p.m. If a viewer turns their television on at a random time during prime time hours, what is the probability that the car commercial will be playing at that time?

To calculate the probability that the car commercial will be playing at a random time during prime time hours, we need to determine the proportion of the total time during prime time hours that the commercial will be playing. The prime time hours are from 8 p.m. to 11 p.m., which is a total of 3 hours or 180 minutes. The commercial is played at 4 random times during prime time. Since the commercial is 90 seconds long, it occupies 90/60 = 1.5 minutes of air time.

Therefore, the total airtime for the commercial is 4 * 1.5 = 6 minutes. To calculate the probability, we divide the airtime of the commercial by the total time during prime time hours:

Probability = (Airtime of the commercial) / (Total time during prime time hours)

Probability = 6 minutes / 180 minutes

Probability ≈ 0.0333

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