00:01
Here we are told that a bank in toronto has found that 66 % of mastercard card holders pay their new monthly balance in full before the payment due date.
00:11
So that's a probability of 0 .66 for any individual cardholder.
00:16
And now we consider six cardholders that are selected at random.
00:21
And we're asked for probabilities that certain numbers out of these six pay their next monthly balance in full before the due date.
00:28
So let's first define a random variable x as the number of cardholders.
00:32
Who pay their balance in full before the due date.
00:36
Now here, each of the six people can be thought of as bernoulli trials with two outcomes of interest, either pay their balance or not before the due date.
00:46
And since it's a random sample, their outcomes are independent.
00:49
The number of successes in a fixed number of independent bernoulli trials is a binomial random variable.
00:56
So here we can say that x is a binomial based on six trials, and probability success on each trial, 0 .66...