Five hundred Year 12 students were surveyed to determine their future plans. Please see the results below.

\begin{tabular}{|l|l|l|l|}
\hline
Year 12 Plans & Male & Female & Total \\
\hline
University & 94 & 208 & 302 \\
\hline
Workforce & 115 & 83 & 198 \\
\hline
Total & 209 & 291 & 500 \\
\hline
\end{tabular}

a) If you were to select a female at random, what is the probability that she will be entering the workforce?



Answer :

To determine the probability that a randomly selected female student will be entering the workforce, we need to follow these steps:

1. Identify the total number of female students: According to the survey, the total number of female students is [tex]\( 291 \)[/tex].

2. Identify the number of female students entering the workforce: The survey results indicate that [tex]\( 83 \)[/tex] female students plan to enter the workforce.

3. Calculate the probability: The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In this case, the favorable outcome is selecting a female student entering the workforce, and the total possible outcome is selecting any female student. Hence, the probability [tex]\( P \)[/tex] is given by:

[tex]\[ P(\text{Female entering the workforce}) = \frac{\text{Number of female students entering the workforce}}{\text{Total number of female students}} \][/tex]

Substituting the numbers from the survey:

[tex]\[ P(\text{Female entering the workforce}) = \frac{83}{291} \][/tex]

4. Compute the probability: Performing the division yields approximately [tex]\( 0.2852233676975945 \)[/tex].

So, the probability that a randomly selected female student will be entering the workforce is approximately [tex]\( 0.2852 \)[/tex] or [tex]\( 28.52\% \)[/tex].