00:01
For this problem, we have been given the values of n and p for a binomial probability distribution, and we need to find certain probabilities.
00:08
So first of all, recall the probability mass function for a binomial random variable x.
00:14
The probability of exactly r successes is given by ncr, p to the power of r, 1 minus p to the power of n minus r.
00:24
So first of all, we want to find the probability of three successes.
00:27
We want to find the probability that x is 3.
00:30
So r will be 3.
00:32
So we have ncr, n is given to be 4, so we have 4c3.
00:35
And p to the power of r, p is given to be 0 .2824, so we have this to the power of 3.
00:41
Then we have 1 minus p to the power of n minus r, so to the power of 4 minus 3.
00:49
Now, if we calculate this, we'll see that this is approximately equal to 0 .065, so this is our required answer, 0 .065...