Aboiler has five identical relief valves. the probability that any particular valve will open on demand is 0.93. assume independent operation of the valves. calculate p(at least one valve opens). (round your answer to eight decimal places.)

There is a 99.99998% probability that at least one valve opens.

Step-by-step explanation:

For each valve there are only two possible outcomes. Either it opens on demand, or it does not. This means that we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which is the number of different combinatios of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.

In this problem we have that:

Calculate P(at least one valve opens).

This is

Either no valves open, or at least one does. The sum of the probabilities of these events is decimal 1. So:

So

Finally

There is a 99.99998% probability that at least one valve opens.