Among 8 electrical components exactly three are known to not

jkminzeszjt

jkminzeszjt

Answered question

2022-02-11

Among 8 electrical components exactly three are known to not function properly. 5 components are randomly selected, how do you find the probability that at least one component does not function properly?

Answer & Explanation

Clark Carson

Clark Carson

Beginner2022-02-12Added 17 answers

Step 1
Out of N=8 components, K=3 are defective and 5 are not defective.
Let X be the number of components that are defective in randomly selected n=5 components
X follows Hypergeometric distribution with parameters N=8, K=3, n=5
Hypergeometric random variable can onlytake integer values in range:
[max(0, n+KN),min(n,K)=[0,3]
P(X1), N=8, K=3, n=5
P(X1)=P(1X3)=1P(X0)=1(P(X=0))
P(X=0)=(K0)(NKn0)(Nn)=(30)(8350)((8)(3))
=(30)(55)(85)=1×156=156=156=0.017857
Answer: =1(0.017857)=0.982143
Use exel function HYPGEOM.DIST (k, n, K, N. cumulative) to calculate
P(X1)=1P(X0)=1PX(0):
1HYPGEOM.DIST(0, 5, 3, 8, TRUE)=0.982142857143
P(X1)=5556=0.9821

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