00:01
Here it is given that the probability of finding an available teller immediately upon arrival at a certain bank is 1 over 4.
00:09
And we are asked to find the probability that the first immediately available teller is on our fifth visit to the bank.
00:17
So let's define a random variable x as the number of visits to the bank required until we find an immediately available teller.
00:36
Now here, each visit to the bank can be seen as a bernoulli trial, where the outcome of success is there is an immediately available teller, and then the outcome of failure is that there is not a teller available immediately.
00:52
So these are bernoulli trials, and we can consider them all to be independent.
00:57
The number of successes, or rather the number of trials required until the first success, is a geometric random variable.
01:06
That is the number of bernoulli trials until the first success is a geometric random variable.
01:11
So here x is a geometric random variable with probability of success 0 .14.
01:22
The probability mass function for the geometric random variable is given by this formula...