00:01
For this exercise, we are told that we are performing independent bernoulli trials, and we are performing four of them.
00:10
The probability of success is 0 .4, and the probability of failure is 0 .6.
00:16
And we are asked to find the probability of at least three successes.
00:23
So let's define random variable x as the number of successes.
00:27
Now, the number of successes and a given number of independent bernoulli trials is a binomial random variable.
00:38
So here, x is a binomial.
00:48
We want the probability of at least three successes, which means the probability that x is greater than or equal to three, and this is equal to one minus the probability of that most of two successes.
01:04
And we can calculate this either using the probability mass function for the binomial random variable or using software such as excel.
01:13
So let's do this one in excel.
01:17
And we will try to calculate this calculation all in one step.
01:22
So if we have 1 minus the probability that x is less than or equal to 2...