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?

Question

2138 views around the world

You can reuse this answer
Creative Commons License

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.!