00:01
We are told in this question that a nuclear reactor has 14 control rods and each control rod acts independently from the others.
00:09
And the probability of activating on demand for each rod is .79.
00:17
In the event of an incident, a meltdown is prevented if at least half the rods are inserted.
00:26
So let's let x be the number of rods that are inserted.
00:46
Here, x is a binomial random variable.
00:49
And we are asked for the probability upon demand that the system will fail.
01:00
So the system is considered failed if less than half the rods perform satisfactory.
01:09
So in other words, what is the probability that x is less than 7? if at least 7 of the rods work, then we do not have a meltdown.
01:23
This is equal to the probability that x is at most 6.
01:28
And we can use software to solve this problem...