To find the probability that a student is an undergraduate student given that they are a science major, we use the concept of conditional probability. The conditional probability \( P(A \mid B) \) is given by:
[tex]\[ P(A \mid B) = \frac{P(A \cap B)}{P(B)} \][/tex]
Here, we are interested in finding the probability that a student is an undergraduate given that they are a science major. Let:
- \( A \) be the event that a student is an undergraduate.
- \( B \) be the event that a student is a science major.
According to the table, we have:
- The number of undergraduate science students (event \( A \cap B \)): 422
- The total number of science students (event \( B \)): 610
So, the conditional probability \( P(\text{undergrad} \mid \text{science}) \) is:
[tex]\[ P(\text{undergrad} \mid \text{science}) = \frac{\text{Number of undergraduate science students}}{\text{Total number of science students}} = \frac{422}{610} \][/tex]
Calculating this division, we get:
[tex]\[ \frac{422}{610} \approx 0.6918032786885245 \][/tex]
Rounding this result to the nearest hundredth, we get:
[tex]\[ 0.69 \][/tex]
Therefore, the probability that a student is an undergraduate given that they are a science major is approximately [tex]\( 0.69 \)[/tex].
