00:01
In this question, we have a binomial distribution.
00:04
We have n equals 13, so there are 13 trials, and p, probability of success, is 0 .69.
00:11
We want the probability that k, the number of successes, is 4.
00:17
So i'm going to use the binomial formula for this question, but you can use something like excel, if you like, or your calculator.
00:25
I'll use the binomial formula.
00:29
Probability of exactly k successes is n, choose k, p to the power of k, one minus p to the power of n minus k.
00:40
So for four successes, we have four successes, we have nine failures, with a total of 13 trials.
00:50
And these are independent trials, which means i can combine their probabilities by multiplication.
00:57
So this term is for these four successes.
01:01
Each has a probability of 0 .69, multiplied by itself.
01:05
Four times.
01:08
This term is for the nine failures, probability of 0 .31, the rest of the time, and multiplied by itself nine times.
01:17
Okay, now i have this probability that the first four trials are successes and the last nine are failures...