Working Women and Computer Use : It is reported that 72% of working women use computers at work.
Choose 5 working women at random. Find

a. The probability that at least 1 does not use a computer at work.
b. The probability that all 5 use a computer in their jobs.


Let $X :$ the number of womens who use computer at work out of $5$.

Here $n = 5$ and $p=0.72$. The probability distribution of $X$ is Binomial distribution. That is $X\sim B(5,0.72)$.

The probability mass function of $X$ is

$$ \begin{aligned} P(X=x) &= \binom{5}{x} (0.72)^x (1-0.72)^{5-x},\\ &\quad x=0,1,\cdots, 5 \end{aligned} $$

a. Probability that at least 1 doesn't use a computer at work is same as the probability that none use computer at work.

$$ \begin{aligned} P(X= 0) & =\binom{5}{0} (0.72)^{0} (1-0.72)^{5-0}\\ & = 0.0017\\ \end{aligned} $$

b. Probability that all 5 use computer at work is

$$ \begin{aligned} P(X= 5) & =\binom{5}{5} (0.72)^{5} (1-0.72)^{5-5}\\ & = 0.1935 \end{aligned} $$

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