00:01
In this question, we have binomial distribution.
00:05
I'm going to let x be the number of successes of n trials, with p probability of success in a single trial.
00:11
So as x follows the binomial distribution with n trials and p probability of success in a single trial, probability of x equals to r when r is the number of successes are n trials, will be n choose r, p to power of r, and 1 minus p to the power of n minus r.
00:31
In part a, our n is 8, p is 0 .25, and our r is 4.
00:45
So we want to find probability of x equals to 4.
00:49
So just sub 4 into the r, and for n will be 8, p is 0 .25.
00:57
So we have n is 8, r is 4, p is 0 .25 to the power of r that is 4.
01:05
And 1 minus p is 0 .75 to the power of n which is 8 minus r which is 4.
01:13
And so we will get this value here, which is 0 .087, 3 decimal place.
01:32
Now in b, we have n is equals to 8, p is 0 .55, and r is 6.
01:51
So we want to find probability x equals to 6.
01:56
So that will be n choose r, so we 8 choose 6, p is 0 .55 to the power of r that is 6, and 1 minus p is 0 .45 to the power of 8 minus 6.
02:11
And so this would be this value here, and that will be 0 .157, 3 decimal place.
02:23
9c, we're given n is 7 p .0 .55.
02:27
So we want to find probability of x less than equals to 3 and less than equals to 5.
02:45
So this would be consists of three mutually exclusive case.
02:50
The first case is x is equals to 3.
02:53
All...