00:01
For this problem, we can consider the number of winning tickets in our set of 20 to be a binomial random variable, where the number of trials is equal to 20, and we're told that the chance of winning a prize for each is 50 -50.
00:17
So, n equals 20, and probability of success is 0 .5.
00:21
Since x is binomial, we have that the probability that x equals a particular value k k is given by n choose k, or n factorial divided by k factorial times n minus k factorial, multiplied by, now it typically would do p to the power of k times 1 minus p to the power of n minus k, but in this case i'll note that since p would be equal to 1 minus p, we can actually simplify this down to just, it would be, when we plug in everything, it's just going to be 0 .5 to the power of 20, because we'd have k plus n minus k, so the total in the exponent would just be n.
01:04
And so, yeah, it just simplifies down to that.
01:08
That being said, we are looking for the chance of winning 15 or more prizes, so probability of x greater than or equal to 15, which would be equal to the sum from k equals 15 up to 20 of probability x equals k.
01:27
So the approach that i'll take here is i'll create a little table of values using my software here...