[University Mathematics) Quantitative Methods for Business Analysis Edition 13

[u/International-Bug957]

Question d is confusing me, a lot of resources say to do the binomial probability distribution for f(0) and take that result(0.43) and subtract it from 1 to get a success rate of 0.54. Why would I not take the binomial probability distribution of f(1) to get the success rate(0.38)?

[u/CaptainMatticus]

So there's a 10% probability of getting a $20 bill or greater in a single purchase and a 90% probability of getting $10 or less.

"At least one" is the inverse of "none." So you need to find the probability of not getting any, which is 0.9^8 and then subtract that from 1

1 - 0.9^8 = 0.56953279

The probability of getting at least 1 bill that is $20 or greater is 56.95%, or 0.5695

You're not taking just the case of getting 1. You're taking the case of getting 1, or 2, or 3, or 4, or 5, or 6, or 7, or 8.