Question

Probability The director of large company is interviewing applicants for two identical jobs. If w = the number of women applicants and m = the

number of men applicants, then the probability that two women are selected for the jobs is $\frac{w}{w+m}·\frac{w-1}{w+m-1}$

(a) Simplify the probability by multiplying the two rational expressions.

(b) Find the probability that two women are selected when $w=5$and $m=10$.

Short answer

Part (a) $\frac{w\left(w-1\right)}{\left(w+m\right)\left(w+m-1\right)}$

Part (b)$\frac{2}{21}=0.09523...$

Step-by-step solution

Part (a) Step 1. Given information

The given expression is$\frac{w}{w+m}·\frac{w-1}{w+m-1}$.

Part (a) Step 2.  Simplify the expression.

$\frac{w}{w+m}·\frac{w-1}{w+m-1}$

Apply the fraction rule.

$\frac{w\left(w-1\right)}{\left(w+m\right)\left(w+m-1\right)}$

Part (b) Step 1. Given information.  

We have,$w=5$and$m=10$

Part (b)  Step 2.  Simplify the expression. 

Consider,

$$\begin{gathered} \frac{w}{w+m}·\frac{w-1}{w+m-1} \\ w=5,m=10 \\ \frac{5}{5+10}·\frac{5-1}{5+10-1} \\ =\frac{1}{3}·\frac{5-1}{5+10-1} \\ =\frac{1}{3}·\frac{2}{7} \\ =\frac{2}{3·\hspace{0.17em}7} \\ =\frac{2}{21} \\ =0.09523... \end{gathered}$$