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A manufacturing plant produces a special kind of car part.

Each car part produced has a 0.087 probability of being defective.
Seven car parts are chosen at random from the production line.

To the nearest thousandth, what is the probability that exactly three of the seven-car parts will be defective?

A. 0.096
B. 0.017
C. 0.009
D. 0.002

Respuesta :

nobillionaireNobley
The probability that exactly x number of cars will be defective is given by

[tex]P(X)={ ^nC_xp^x(1-p)^{n-x}[/tex]

Here p = 0.087, n = 7, x = 3

[tex]P(3)={ ^7C_3(0.087)^3(1-0.087)^{7-3}} \\ \\ =35(0.087)^3(0.913)^4=35(0.000658503)(0.694837) \\ \\ =0.016[/tex]

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