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For two programs at a university, the number of students for two majors is as follows.

[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline
& History & Science & Total \\
\hline
Undergraduate & 390 & 422 & 812 \\
\hline
Graduate & 73 & 188 & 261 \\
\hline
Total & 463 & 610 & 1073 \\
\hline
\end{tabular}
\][/tex]

Find the probability that a student is a science major, given they are a graduate student.

[tex]\[
P(\text{science} \mid \text{graduate}) = \frac{P(\text{science and graduate})}{P(\text{graduate})} = \frac{188}{261} \approx 0.72
\][/tex]

Round to the nearest hundredth: 0.72



Answer :

GinnyAnswer
To find the probability that a student is a science major given that they are a graduate student, we can use the formula for conditional probability:

[tex]\[ P (\text{science} \mid \text{graduate}) = \frac{P(\text{science and graduate})}{P(\text{graduate})} \][/tex]

1. Determine [tex]\( P(\text{science and graduate}) \)[/tex]:

The number of graduate students majoring in science is given as 188.

2. Determine [tex]\( P(\text{graduate}) \)[/tex]:

The total number of graduate students is given as 261.

3. Calculate the conditional probability:

[tex]\[ P (\text{science} \mid \text{graduate}) = \frac{188}{261} \][/tex]

4. Perform the division to find the exact probability:

[tex]\[ P (\text{science} \mid \text{graduate}) \approx 0.7203065134099617 \][/tex]

5. Round to the nearest hundredth:

[tex]\[ P (\text{science} \mid \text{graduate}) \approx 0.72 \][/tex]

Therefore, the probability that a student is a science major given that they are a graduate student, rounded to the nearest hundredth, is 0.72.

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