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.
Solution
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
$$ \begin{aligned} P(X= 5) & =\binom{5}{5} (0.72)^{5} (1-0.72)^{5-5}\\ & = 0.1935 \end{aligned} $$
Further Reading
- Statistics
- Descriptive Statistics
- Probability Theory
- Probability Distribution
- Hypothesis Testing
- Confidence interval
- Sample size determination
- Non-parametric Tests
- Correlation Regression
- Statistics Calculators
