Defective cars

The company has produced 500,000 cars so far, of which 5,000 were defective. What is the probability that at most one car out of 50 cars in daily production will be defective?

Final Answer:

p =  0.9106

Step-by-step explanation:

$$\begin{gathered} r=\frac{5000}{500000}=\frac{1}{100}=0.01 \\ {p}_0=\left(\genfrac{}{}{0ex}{}{50}{0}\right)\cdot r^0\cdot (1-r{)}^{50-0}=(\genfrac{}{}{0ex}{}{50}{0})\cdot 0.01^0\cdot (1-0.01{)}^{50-0}=1\cdot 0.01^0\cdot 0.99^{50}\doteq 0.605 \\ {p}_1=\left(\genfrac{}{}{0ex}{}{50}{1}\right)\cdot r^1\cdot (1-r{)}^{50-1}=(\genfrac{}{}{0ex}{}{50}{1})\cdot 0.01^1\cdot (1-0.01{)}^{50-1}=50\cdot 0.01^1\cdot 0.99^{49}\doteq 0.3056 \\ p=p_0+p_1=0.605+0.3056=0.9106 \end{gathered}$$

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