00:01
And this problem here we are given that 60 % of the people who enter a shoe store make a purchase.
00:12
So for a person entering the shoe store, the probability that they would make a purchase is 60 % which is 60 over 100.
00:26
And we can write that as 0 .6.
00:30
And for a person who has entered the store let y denote the random variable such that y equals one if they buy something and y equals zero otherwise so here y is a bernoli trial with success probability 0 .6 because y equals 1 if with probability 0 .6 because y equals 1 if with probability 0 .0 now when we have 12 people entering the store, we have 12 independent bernoulli trials.
01:19
So the random variable x, denoting the number of people who make a purchase, follows a binomial distribution with parameters n equals 12 and p equals 0 .6.
01:47
We want to find the probability that at least 10 people have made a purchase out of the 12 people who entered the shop.
02:00
That is, we want the probability that x is greater than equal to 10.
02:05
But x can be at most 12, so probability x greater than equal to 10 is simply probability of x equals 10 plus probability of x equals 11 plus probability of x equals 12.
02:18
Now remember that x follows a binomial distribution with parameters n equals 12 and p equals 0 .6...