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

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Answer 1 · 2017-10-21T20:05:23

# 3125/32768.#

Let us call the event #S# that a randomly selected component

functions properly, Success.

Then, clearly, the Prob. of Success # P(S)=p=(""_5C_1)/(""_8C_1)=5/8.#

#:. q=1-p=3/8.#

If, #X# denotes the no. of success in a series of #n# trials, then, #X#

is a Binomial Random Variable with parameters #n=5, &, p=5/8.#

#:. P(X=x)=p(x)=""_nC_xp^xq^(n-x), where, x=0,1,2,...,n,#

#=""_5C_x(5/8)^x(3/8)^(5-x), where, x=0,1,2,...,5.#

#"Now, the Reqd. Prob.="P(X=5)=""_5C_5(5/8)^5(3/8)^0.

# rArr" The Reqd. Prob.="3125/32768.#

Enjoy Maths.!