Question

A k out of n system is one in which there is a group of n components, and the system will function if at least k of the components function. For a certain 4 out of 6 system, assume that on a rainy day each component has probability 0.4 of functioning, and that on a nonrainy day each component has probability 0.8 of functioning.

a) What is the probability that the system functions on a rainy day?

b) What is the probability that the system functions on a nonrainy day? Round the answer to five decimal places.

c) Assume that the probability of rain tomorrow is 0.20. What is the probability that the system will function tomorrow?

Answer 1

a)

here this is binomial with parameter n=6 and p=0.4

probability that the system functions on a rainy day :

P(X>=4)=1-P(X<=3)=

1-∑x=0x-1   (nCx)px(q)(n-x) =

0.179200

b)

this is binomial with parameter n=6 and p=0.8

probability that the system functions on a nonrainy day

P(X>=4)=1-P(X<=3)=

1-∑x=0x-1   (nCx)px(q)(n-x) =

0.901120

c)

P(system function) =P(rainy day)*P(function|rainy day)+P(non rainy day)*P(function|non rainy day)

=0.2*0.179200+0.8*0.901120 =0.756736