Given:

\(\begin{array}{c|cc|c} &\text{Physics}&\text{Chemistry}&\text{Total}\\ \hline \text{Males}&100&68&168\\ \text{Females}&71&61&132\\ \hline \text{Total}&171&129&300 \end{array}\)

We note that 132 of the 300 seniors in the table are female.

The probability is the number of favorable outcomes divided by the number of possible outcomes:

\(P(Female)=\frac{\text{# of favorable outcomes}}{\text{# of possible outcomes}}=\frac{132}{300}\)

We note that 168 of the 300 seniors in the table are female and are enrolled in physics. \(P(\text{Female and physics})=\frac{\text{# of favorable outcomes}}{\text{# of possible outcomes}}=\frac{71}{300}\)

Let us use the definition Conditional probability: \(P(B|A)=\frac{P(A\cap B)}{P(A)}=\frac{P(\text{A and B})}{P(A)}\)

\(P(\text{physics|Female})=\frac{P(\text{Female and physics})}{P(\text{Female})}\)

\(=\frac{\frac{71}{300}}{\frac{132}{300}}\)

\(=\frac{71}{132}\)

\(\approx0.5379\)

\(=53.79\%\)

Result : \(\frac{71}{132}=\approx0.5379=53.79\%\)