#### dr_feeels

##### New Member
Q:
Many employers are finding that some of the people they hire are not who and what they claim to be. This has led to a boom of companies providing credential checking services. Suppose that your company is recruiting new staff and you receive five applications for the advertised position. Further, suppose that the probability that an applicant would falsify information on his/her application form is 0,15. Assume that applicants falsify information on their application forms independently of each other. What is the probability that at least one of the five application forms has been falsified?

So I thought this may relate to a conditional probability question: 0,15 people are likely to falsify info, what is the probability that at least 1 of the 5 DO falsify.
I've tried so many equations and nothing worked out, the textbook gives the final rounded answer to 0,556.
HELP ME PLS

#### Editor

##### New Member
you can use binomial probability to calculate the probability of no one is submitting false information i.e 0.44 and minus it from 1 for atleast one gives false information .you can refer the following book for more info
www.ijsmi.com/book.php

#### Con-Tester

##### Member
You can turn the problem around by asking what the probability is that none of the five people submits false information. If the probability is p = 0.15 that a given applicant submits false information, then the probability that s/he won’t is p’ = 1 – p = 1 – 0.15 = 0.85.

For five independent applicants, the probability that none of them submits false information is then P’ = 0.85×0.85×0.85×0.85×0.85 = 0.85⁵ = 0.4437053125. Consequently, the probability that at least one applicant submits false information is P = 1 – 0.4437053125 = 0.5562946875 ≈ 0.556.

The above approach is essentially identical to the one @Editor proposed, but with more explanatory detail.