Probability of failures

In certain productions, the probability of failures is 0.01. Calculate the probability that there will be more than one failure among the 100 selected products if we return the selected products to the file after the check.

Correct answer:

p =  0.2642

Step-by-step explanation:

$$\begin{gathered} C_0(100)=\left({\displaystyle \genfrac{}{}{0px}{}{100}{0}}\right)={\displaystyle \frac{100!}{0!(100-0)!}}={\displaystyle \frac{1}{1}}=1 \\ {C}_1(100)=\left({\displaystyle \genfrac{}{}{0px}{}{100}{1}}\right)={\displaystyle \frac{100!}{1!(100-1)!}}={\displaystyle \frac{100}{1}}=100 \\ q=0.01 \\ n=100 \\ {p}_0=\left(\genfrac{}{}{0px}{}{n}{0}\right)\cdot q^0\cdot (1-q{)}^{n-0}=1\cdot 0.01^0\cdot (1-0.01{)}^{100-0}\doteq 0.366 \\ {p}_1=\left(\genfrac{}{}{0px}{}{n}{1}\right)\cdot q^1\cdot (1-q{)}^{n-1}=100\cdot 0.01^1\cdot (1-0.01{)}^{100-1}\doteq 0.3697 \\ p=1-(p_0+p_1)=1-(0.366+0.3697)=0.2642 \end{gathered}$$

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