Question

Out of $100$ bicycles, $10$ bicycles have puncture. What is the probability of not having any punctured bicycle in a sample of $5$ bicycles?

• A. $\frac{1}{2^9}$
• B. ${\left(\frac{9}{10}\right)}^5$
• C. $\frac{1}{{10}^5}$
• D. $\frac{1}{2^5}$

Answer 1

The correct option is B ${\left(\frac{9}{10}\right)}^5$

Here, $n=5$, $r=0$, $p=\frac{10}{100}$, $q=\frac{90}{100}$

Now, $P(X=0){=}^n{C}_r{p}^r{q}^{n-r}$

${=}^5{C}_0{\left(\frac{10}{100}\right)}^0{\left(\frac{90}{100}\right)}^{5-0}$

$=1\times 1\times {\left(\frac{9}{10}\right)}^5={\left(\frac{9}{10}\right)}^5$.