A random sample of 2,500 people was selected, and the people were asked to give their favorite season. Their responses, along with their age group, are summarized in the two-way table below. begin{array}{c|cccc|c} & text {Winter} &text{Spring}& text {Summer } & text {Fall}& text {Total} hline text {Children} & 30 & 0 & 170&0&200 text{Teens} & 150 & 75 & 250&25&500 text {Adults } & 250 & 250 & 250&250&1000 text {Seniors} & 300 & 150 & 50&300&800 hline text {Total} & 730 & 475 & 720 &575&2500 end{array} Among those whose favorite season is spring, what proportion are adults? a) frac{250}{1000} b) frac{250}{2500} c) frac{475}{2500} d) frac{250}{475} e) frac{225}{475}

A random sample of 2,500 people was selected, and the people were asked to give their favorite season. Their responses, along with their age group, are summarized in the two-way table below. begin{array}{c|cccc|c} & text {Winter} &text{Spring}& text {Summer } & text {Fall}& text {Total} hline text {Children} & 30 & 0 & 170&0&200 text{Teens} & 150 & 75 & 250&25&500 text {Adults } & 250 & 250 & 250&250&1000 text {Seniors} & 300 & 150 & 50&300&800 hline text {Total} & 730 & 475 & 720 &575&2500 end{array} Among those whose favorite season is spring, what proportion are adults? a) frac{250}{1000} b) frac{250}{2500} c) frac{475}{2500} d) frac{250}{475} e) frac{225}{475}

Question
Two-way tables
asked 2020-11-26
A random sample of 2,500 people was selected, and the people were asked to give their favorite season. Their responses, along with their age group, are summarized in the two-way table below.
\(\begin{array}{c|cccc|c} & \text {Winter} &\text{Spring}& \text {Summer } & \text {Fall}& \text {Total}\\ \hline \text {Children} & 30 & 0 & 170&0&200 \\ \text{Teens} & 150 & 75 & 250&25&500 \\ \text {Adults } & 250 & 250 & 250&250&1000 \\ \text {Seniors} & 300 & 150 & 50&300&800 \\ \hline \text {Total} & 730 & 475 & 720 &575&2500 \end{array}\)
Among those whose favorite season is spring, what proportion are adults?
\(a) \frac{250}{1000}\)
\(b) \frac{250}{2500}\)
\(c) \frac{475}{2500}\)
\(d) \frac{250}{475}\)
\(e) \frac{225}{475}\)

Answers (1)

2020-11-27

Step 1
Obtain the proportion of adults whose favourite season is spring:
The value of probability is obtained by:
\(P(E)=\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}\)
\(P(\text{Adults whose favorite season is spring})=\frac{\text{Number of adults whose favorite season is spring}}{\text{Total number of outcomes}}\)
\(=\frac{250}{2500}\)
Step 2
Therefore, the correct answer is “Option B.) \(\frac{250}{2500}\).

0

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