00:01
In this problem, it is said that four identical machines are kept for safety in case of failure, and the chance of each one failing is 0 .05 and they are independent.
00:11
Now, based on this, we need to determine some probabilities.
00:14
Now, first of all, let us consider f to be the event that a machine fails.
00:19
Then in the question, it is given that the probability of this event f is 0 .05.
00:25
Now, from here, we can determine p of f complement, which is the probability that a machine does not fail.
00:31
And using the complement rule of probability, this will be equal to 1 minus p of f.
00:36
So we get 1 minus 0 .05, and that is equal to 0 .95.
00:42
Now, the first question is, what is the probability that all four fail? so that means we need to find the probability that the first machine fails and the second machine fails and the third machine fails and the fourth machine also fails.
00:57
Now it is said that the chance of each one failing is 0 .05 and they are independent.
01:02
Because of that, all of these events are independent events.
01:07
And because of that, we can use the multiplication rule of probability for independent events.
01:11
According to which, this will be equal to p of f times p of f times p of f times p of f.
01:19
So that's p of f multiplied by itself four times.
01:23
So that's p of f hold to the power of four.
01:25
And p of f is 0 .05.
01:27
So we have 0 .05 hold to the power of 4.
01:32
If we calculate that, this is equal to 0 .00 -0 -0 -625...