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.

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MrRoyal MrRoyal · Answer 1 · 2022-02-02T11:13:00+01:00

The probability that if 5 tires are inspected, exactly 2 have a defect is 0.021

The given parameters are:

[tex]p = 5\%[/tex] --- the proportion that contains defect

[tex]n =5[/tex] --- the sample size

[tex]r =2[/tex] -- the selected sample

The probability is then calculated as:

[tex]P(x =r) = ^nC_r * p^r * (1 - p)^{n-r}[/tex]

So, we have:

[tex]P(x =2) = ^5C_2 * (5\%)^2 * (1 - 5\%)^{5-2}[/tex]

[tex]P(x =2) = 10 * (5\%)^2 * (1 - 5\%)^3[/tex]

[tex]P(x =2) = 0.021[/tex]

Hence, the probability that if 5 tires are inspected, exactly 2 have a defect is 0.021