burgular alarm system has six fail-safe components. the probability of each failing is 0.05. Find these probabilities a)Exactly three will fail b) Fewer than two will fail. c) None will fail. d) Compare the answers from a,b,and c and explain why the results are reasonable

Question

anonymous · Answer

So are these independent fail-safes, or are they sequential where one must die before the others have a chance to work?

anonymous · Answer

If they're independent then we have a binomial distribution.

anonymous · Answer

$$
X\sim B(n=6,p=0.5)\implies P(X=k) = \binom 6k(0.05)^k(1-0.05)^{6-k}
$$

anonymous · Answer

a)  $Pr(X=3)$
b) $\Pr(X<3) =Pr(X=0)+Pr(X=1) $
c) $\Pr(X=0)$

anonymous · Answer

Plug and chug.

anonymous · Answer

thanks so much for your help