Question 8 (1 point)A tire manufacturer knows that 5% of tires contain a defect, and the presence of a defect is independent from tire to tire.What is the probability that if 5 tires are inspected, exactly 2 have a defect?Round to 3 decimal places.Blank 1:

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ANSWER:

The probability is 0.018

STEP-BY-STEP EXPLANATION:

That 5% are defective means that 5 out of 100 tires are defective.

If 5 tires are selected, the probability that they are exactly defective is calculated as follows

[tex]\begin{gathered} P(X=k)=\frac{5Ck\cdot95C5-k}{100C5},\text{ for k = 2} \\ \end{gathered}[/tex]

Now, resolving

[tex]\begin{gathered} 5C2=\frac{5!}{2!\cdot(5-2)!}=10 \\ 95C3=\frac{95!}{3!\cdot(95-3)!}=138415 \\ 100C5=\frac{100!}{5!\cdot\left(100-5\right)!}=75287520 \end{gathered}[/tex]

replacing:

[tex]\begin{gathered} P(X=2)=\frac{10\cdot138415}{75287520} \\ P(X=2)=0.018 \end{gathered}[/tex]