Question

To avoid unpleasant surprises when the statement comes, you try to record all of your credit card transactions in a ledger. Unfortunately, you tend to neglect recording about 5% of your purchases. Suppose last month you had 25 purchases on your credit card account. When the statement arrives, you count the number of purchases you forgot to record. The random variable X represents the number of unrecorded purchases in a month with 25 transactions. Explain WHY this is a binomial experiment.

Answer 1

it is binomial experiment because it has n trials, i.e. 25 trials and every trial has some probability of being recorded or unrecoded. It is also clear that the probability of being recorded or unrecorded for each trial is same, i.e. the probability for each trial is not changing. There are exactly two outcomes for each trial, either it is recorded or it is unrecorded.

So, it met all the four conditions of binomial experiment, thus we can say that it is a perfect example of binomial experiment.