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.
