00:01
In this question, we are given that an accounting company prepare a yearly budget for a small company, and probability of making zero error is 0 .5, one error will be 0 .28, 2 errors will be 0 .15, and 3 errors will be 0 .07.
00:20
And 20 companies have the firm prepare their budgets.
00:23
I'm going to let e1, e2, e3, e4 denote the events of the company making 0, 1, 2 and 3, errors respectively.
00:32
So this is probability e1 and this is probability e2 and this is probability e3 and this is probability e4.
00:48
Now i'm going to let x1, x2, x3, x4 be the random variable representing the number of occurrences for events, e1, e2, e3 and e4.
00:57
Now we want to find probability out of the 20 companies, 9 will contain zero errors, six will contain one error, three will contain two errors and two will contain three errors.
01:11
Now we're looking at the multi -normal distribution where there are k outcomes in e1, e2 up to ek events with probability p1, p2 up to pk.
01:24
So this is probability p1, this is p2, this is p2, this is p4.
01:34
And x1, x2, up to xk represent the number of occurrences for the events, e1, e2, up to ek in n independent trials.
01:45
Now in this case, we have 20 companies, so we have 20 trials.
01:49
So our n is equal to 20.
01:55
And probability x equals to x1.
01:59
So our small x1 and there's x1 occurrence and x2 is equal.
02:07
Equals to small x2, that's x2 occurrence, all the way to xk occurrence.
02:13
So this probability will be n factorial divided by x1 factorial, x2 factorial, all the way to xk factorial, times p1 to the power x1, p2 to power x2, all the way to p k to power xk...