Question

# Use the two-way table below to answer the following question. Round the answer to the nearest whole percent. There are 300 seniors at Bellmere Senior

Two-way tables

Use the two-way table below to answer the following question. Round the answer to the nearest whole percent. There are 300 seniors at Bellmere Senior High School who are enrolled in elective science classes as shown below.
$$\begin{array}{c|cc|c} &\text{Physics}&\text{Chemistry}&\text{Total}\\ \hline \text{Males}&100&68&168\\ \text{Females}&71&61&132\\ \hline \text{Total}&171&129&300 \end{array}$$
What is the probability that a senior student chosen at random is enrolled in physics given that student is female?

2021-02-01

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 : $$\frac{71}{132}=\approx0.5379=53.79\%$$