00:01
Here we have a binomial random variable x based on 10 trials and probability of success, 0 .6.
00:09
And we are asked to calculate 4 or 5 probabilities.
00:13
The first one is the probability that x is equal to 2.
00:20
Now the probability mass function for the binomial random variable is given by this formula.
00:40
And so to solve the probability that x equals 2, we can use the probability mass function.
00:45
So we have 10 choose 2 times 0 .6 to the exponent 2 times 0 .4 to the exponent 8.
00:57
And this comes out to approximately 0 .01 .6.
01:05
And then for b we have the probability that x is greater than 10.
01:13
Now notice for the binomial random variable, x can be any integer from 0 up to the number of trials.
01:23
So x is not defined for, or the random variable has no outcomes which are greater than 10.
01:31
So the probability that x is greater than 10, therefore must be 0.
01:38
And then for c, we want the probability that x is between 3 and 6 exclusive.
01:49
This is the same as the probability that x is between 4 and 5 inclusive.
01:58
And this is equal to the probability that x equals 4 plus the probability that x equals 5.
02:04
So using the probability mass function, we would have for x equals 4, the first term would be 10 choose 4 times 0 .6 to the exponent 4.
02:14
Times 0 .4 to the exponent 6.
02:18
And then the second term for x equals 5, we have 10 choose 5 times .6 to the exponent 5 times 0 .4 to the exponent 5.
02:31
And this comes out to approximately .31 to 1.
02:40
And for d we want the probability that x is between 5 and 9.
02:49
This can be re -expressed as the probability that x is at most 8, minus the probability that x is at most 5.
03:01
And let's use software to solve this problem.
03:04
So we have two terms...