Looking at the question we can see that it says:
We should know what these symbols mean:
stands for something less than the other, for example:
We can say that 2 is less than 5 so in a symbolic form it can be written as,
Similarly,
stands for something greater than the other, for example:
We can say that 7 is greater than 5, in a symbolic form it can be written as,
So here, means that, 42153 is greater than 35214.
Answer:
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.