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In an assembly-line production of industrial robots, gearbox assemblies can be installed in one minute each if holes have been properly drilled in the boxes and in ten minutes if the holes must be redrilled. Twenty-one gearboxes are in stock, 4 with improperly drilled holes. Five gearboxes must be selected from the 21 that are available for installation in the next five robots. (Round your answers to four decimal places.) (a) Find the probability that all 5 gearboxes will fit properly.

Respuesta :

Answer: Our required probability is 0.304.

Step-by-step explanation:

Since we have given that

N = 21

Number of improperly drilled holes k = 4

Number of properly drilled holes = N-k= 21-4=17

Let X be the number of improperly drilled holes in a sample of 5.

We will use "Binomial distribution":

[tex]P(X=5)=\dfrac{^4C_0\times ^{17}C_5}{^{21}C_5}=0.304[/tex]

So, our required probability is 0.304.

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