Use the rule of total probability to find the indicated probability.
-Among students at one college are 3874 women and 3058 men. The following table provides relative-frequency distributions for subject major for males and females at the college. $$\begin{array} { l c c }
\text { Major } & \begin{array} { l }
\text { Relative frequency } \
\text { for women }
\end{array} & \begin{array} { l }
\text { Relative frequency } \
\text { for men }
\end{array} \
\hline \text { Humanities } & 0.187 & 0.165 \
\text { Science } & 0.284 & 0.349 \
\text { Social Science } & 0.142 & 0.179 \
\text { Other } & 0.387 & 0.307
\end{array}$$ A student is selected at random from the college. Determine the probability that the student is a Science major.
A)0.317
B)0.159
C)0.313
D)0.320

Question

Use the rule of total probability to find the indicated probability.
-Among students at one college are 3874 women and 3058 men. The following table provides relative-frequency distributions for subject major for males and females at the college. $$\begin{array} { l c c } 
\text { Major } & \begin{array} { l } 
\text { Relative frequency } \
\text { for women }
\end{array} & \begin{array} { l } 
\text { Relative frequency } \
\text { for men }
\end{array} \
\hline \text { Humanities } & 0.187 & 0.165 \
\text { Science } & 0.284 & 0.349 \
\text { Social Science } & 0.142 & 0.179 \
\text { Other } & 0.387 & 0.307
\end{array}$$ A student is selected at random from the college. Determine the probability that the student is a Science major. 
A)0.317
B)0.159
C)0.313
D)0.320

Quizplus · Accepted Answer

The probability that a randomly selected student is a Science major can be calculated using the rule of total probability. This involves taking the weighted average of the probabilities of being a Science major among women and men, weighted by the proportion of women and men in the college. The calculation is as follows:$$P(\text{Science}) = P(\text{Science}|\text{Woman})P(\text{Woman}) + P(\text{Science}|\text{Man})P(\text{Man})$$Given:- Total students = 3874 women + 3058 men = 6932- $P(\text{Science}|\text{Woman}) = 0.284$- $P(\text{Science}|\text{Man}) = 0.349$- $P(\text{Woman}) = \frac{3874}{6932}$- $P(\text{Man}) = \frac{3058}{6932}$$$P(\text{Science}) = 0.284 \times \frac{3874}{6932} + 0.349 \times \frac{3058}{6932} \approx 0.313$$Therefore, the probability that a randomly selected student is a Science major is approximately 0.313.

Use the Rule of Total Probability to Find the Indicated