Question

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:

Answer 1

The probability is 0.018

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

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

Now, resolving

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

replacing:

`\begin{gathered} P(X=2)=(10\cdot138415)/(75287520) \\ P(X=2)=0.018 \end{gathered}`