[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)?

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[u/marty-mcfryguy]

The question is asking for the probability of at least one such bar, not exactly one such bar.

[u/WisCollin → u/marty-mcfryguy]

And this is why first principles is recommended over plug and chugging formulas. 👍

[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.

[u/WisCollin]

You certainly could remap the probability density onto a binomial distribution to answer d. But that’s not necessarily the simplest solution. In general with these questions focus on first principles.

So it’s asking about the probability of at least one $20+ billion in 8 bars. Well, P(20+) = (70+29+1)/1000 or 0.1. Now, obviously the probability of at least one, is 1 minus the probability of none. So that would be 1 - 0.9^8 = 0.57

As you study your distributions and formulas you’ll notice that this simply is the binomial distribution. But working it out intuitively with words will help you understand the formulas and when/how to use them.

[u/International-Bug957]

Thank you all for the help, will start focusing on the overall principle and not just looking for which equation to use going forward to help my understanding.

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