An online poll asked people how likely they were to see a new movie that was coming out in the summer.Here's how they responded: $$\begin{array} { l | l }
\text { Response } & \text { Number } \
\hline \text { Will definitely see it } & 215 \
\text { Will probably see it } & 268 \
\text { Will probably not see it } & 349 \
\text { Will definitely not see it } & 374 \
\hline \text { Total } & 1206
\end{array}$$ Let's call someone who responded that they would definitely or probably see it a "likely viewer" and the other two categories,"unlikely viewer." If we select two people at random from this sample,what is the probability that both are likely viewers?

Question

An online poll asked people how likely they were to see a new movie that was coming out in the summer.Here's how they responded: $$\begin{array} { l | l } 
\text { Response } & \text { Number } \
\hline \text { Will definitely see it } & 215 \
\text { Will probably see it } & 268 \
\text { Will probably not see it } & 349 \
\text { Will definitely not see it } & 374 \
\hline \text { Total } & 1206
\end{array}$$ Let's call someone who responded that they would definitely or probably see it a "likely viewer" and the other two categories,"unlikely viewer." If we select two people at random from this sample,what is the probability that both are likely viewers?

Quizplus · Accepted Answer

There are a total of 60 people in the sample size. Among them, there are 19 likely viewers and 41 unlikely viewers.
To find the probability that two people selected at random are both likely viewers, we need to use the formula for probability of independent events:
P(both likely viewers) = P(1st person is a likely viewer) × P(2nd person is also a likely viewer, given that the 1st person was a likely viewer).
For the first person, the probability of being a likely viewer is 19/60.
For the second person, given that the first person was a likely viewer, the probability of being a likely viewer is 18/59 (there are now only 18 likely viewers left out of the remaining 59 people).
Therefore, P(both likely viewers) = (19/60) × (18/59) = 0.161 (rounded to three decimal places).
Hence, the best choice is A).

An Online Poll Asked People How Likely They Were to See