PROBLEM 14E

In Example 1.4-5, suppose that the probability of failure of a component is p = 0.4. Find the probability that the system does not fail if the number of redundant components is

(a) 3.

(b) 8.

References Example 1.4-5

Answer :

Step 1 of 2 :

Probability of failure of component is p=0.4

Let number of redundant is n.

P(system does not fail) =

P(system does not fail) =

P(system does not fail) =

a).

Now we have to find the probability that the system does not fails.

If the number of redundant is 3.

P(system does not fail) =

Here n=3 and p=0.40

Substitute n and p values.

P(system does not fail) =

P(system does not fail) =

P(system does not fail) =

Therefore the probability that the system does not fails is 0.936