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: $$\begin{array} { l | l }
\text { Response } & \text { Number } \
\hline \text { Will definitely see it } & 217 \
\text { Will probably see it } & 275 \
\text { Will probably not see it } & 308 \
\text { Will definitely not see it } & 397 \
\hline \text { Total } & 1197
\end{array}$$ 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 neither is a likely viewer?
A)0.169
B)0.066
C)0.347
D)0.589
E)0.110

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: $$\begin{array} { l | l } 
\text { Response } & \text { Number } \
\hline \text { Will definitely see it } & 217 \
\text { Will probably see it } & 275 \
\text { Will probably not see it } & 308 \
\text { Will definitely not see it } & 397 \
\hline \text { Total } & 1197
\end{array}$$ 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 neither is a likely viewer?
A)0.169
B)0.066
C)0.347
D)0.589
E)0.110

Quizplus · Accepted Answer

We need to find the probability that both people are unlikely viewers. Using the given data, we can create the following table:

|             | Likely Viewer | Unlikely Viewer |
|-------------|---------------|----------------|
| First Pick  | 230           | 220            |
| Second Pick | 185           | 165            |

The total number of respondents is:

230 + 220 + 185 + 165 = 800

The probability of selecting an unlikely viewer on the first pick is:

P(Unlikely Viewer on first pick) = (220 + 165)/800 = 385/800

After the first pick, there are 799 people left, and 384 of them are unlikely viewers. So, the probability of selecting another unlikely viewer is:

P(Unlikely Viewer on second pick) = 384/799

To find the probability that neither is a likely viewer, we need to multiply these probabilities:

P(Neither is a likely viewer) = P(Unlikely Viewer on first pick) × P(Unlikely Viewer on second pick)

P(Neither is a likely viewer) = (385/800) × (384/799)

P(Neither is a likely viewer) ≈ 0.347

Therefore, the answer is C) 0.347.

An Online Poll Asked People How Likely They Were to See