# After being rejected for employment, Kim Kelly learns that the Bellevue Credit C

After being rejected for employment, Kim Kelly learns that the Bellevue Credit Company has hired only two women among the last 19 new employees. She also learns that the pool of applicants is very large, with an approximately equal number of qualified men as qualified women.
Help her address the charge of gender discrimination by finding the probability of getting two or fewer women when 19 people are hired, assuming that there is no discrimination based on gender.
(Report answer accurate to 8 decimal places).

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Margot Mill

Step 1
The binomial probability distribution is,
$$P(X=x)=\left(\begin{array}{c}n\\ x\end{array}\right)(p)^{x}(1-p)^{n-x}$$
In the formula, n denotes the number of trails, p denotes probability of success, and x denotes the number of success.
Let x be the number of women hired which follows binomial with sample size 19 and probability of success $$\displaystyle{0.5}{\left(={\frac{{{1}}}{{{2}}}}\right)}$$
Step 2
The probability of getting two or fewer women when 19 people are hired is,
$$\displaystyle{P}{\left({X}\leq{2}\right)}={P}{\left({X}={0}\right)}+{P}{\left({X}={1}\right)}+{P}{\left({X}={2}\right)}$$
$$=\left(\begin{array}{c}19\\ 0\end{array}\right)(0.5)^{0}(1-0.5)^{19-0}+\left(\begin{array}{c}19\\ 1\end{array}\right)(0.5)^{1}(1-0.5)^{19-1}+\left(\begin{array}{c}19\\ 2\end{array}\right)(0.5)^{2}(1-0.5)^{19-2}$$
$$\displaystyle={0.00000191}+{0.00003624}+{0.00032616}$$
$$\displaystyle={0.00036431}$$
Thus, the probability of getting two or fewer women when 19 people are hired is 0.00036431.