Video Transcript
A sample of 64 people found that 36
of them watch Channel A, 29 of them watch Channel B, and 11 watch both channels. What is the probability that a
random person from the sample only watches Channel A?
In this question, we are told that
a sample of 64 people is taken about the viewing habits of two channels. We are told the number of people
who watch each channel and how many watch both channels. We want to determine the
probability that a randomly selected person from the sample only watches Channel
A. To do this, we can start by
recalling that the probability of choosing a person who only watches Channel A from
the sample is given by the number of people who only watch Channel A in the sample
divided by the total number of people in the sample.
To determine the number of people
who only watch Channel A in the sample, we note that 36 people in total watch
Channel A, and of these 11 people also watch Channel B. So the difference in these values
gives the number of people who only watch Channel A. This means that in the sample, 25
people only watch Channel A.
Finally, we are told that there are
64 people in the sample. So the probability of choosing
someone in the sample who only watches Channel A is 25 over 64.
