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nataly862011 [7]
2 years ago
8

In a production process, the probability of manufacturing a defective rear view mirror for a car is 0.075. Assume that the quali

ty status of any rear view mirror produced in this process is independent of the status of any other rear view mirror. A quality control inspector is to examine rear view mirrors one at a time to obtain three defective mirrors. Determine the probability that the third defective mirror is the 10th mirror examined.
Mathematics
1 answer:
Leviafan [203]2 years ago
5 0

Answer:

The probability that the 3rd defective mirror is the 10th mirror examined = 0.0088

Step-by-step explanation:

Given that:

Probability of manufacturing a defective mirror = 0.075

To find the probability that the 3rd defective mirror is the 10th mirror examined:

Let X be the random variable that follows a negative Binomial expression.

Then;

X \sim  -ve  \ Bin (k = 3 , p = 0.075)\\ \\ P(X=x)= \bigg (^{x-1}_{k-1}\bigg)\times P^k\times (1-P)^{x-k}

= \bigg (^{10-1}_{3-1}\bigg)\times 0.075^3\times (1-0.075)^{10-3}

= \bigg (^9_2\bigg)\times 0.075^3\times (1-0.075)^{7}

= \dfrac{9!}{2!(9-2)!}\times 0.075^3\times (0.925)^{7}

= \dfrac{9*8*7!}{2!(7)!}\times 0.075^3\times (0.925)^{7}

= 0.0087999

≅ 0.0088

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