Becoming successful is not luck. It’s math.

If your probability of success is 1/100 and you try 100 times, you have a 100% chance of success.

For whatever reason many people decided this mistake had to be corrected. So one might ask: what is the actual chance of success? How many tries (rounded to the nearest 100) would give you a 99% chance of success?

As usual, watch the video for a solution.

Post About The Math Of Becoming Successful

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Answer To Post About The Math Of Becoming Successful

(Pretty much all posts are transcribed quickly after I make the videos for them–please let me know if there are any typos/errors and I will correct them, thanks).

Let p = chance of success and 1 – p = failure. Then for n independent trials, the chance you have at least 1 success is:

Pr(at least 1 success in n trials)
= 1- Pr(all failures in n trials)
= 1- Pr(failure trial 1)Pr(failure trial 2)…Pr(failure trial n)
= 1 – (1 – p)ⁿ

For p = 1/100 and n = 10 we have:

= 1 – (1 – 1/100)¹⁰⁰
= ≈ 63.4%

In spite of 100 trials, you still have about a 36.6% chance of failure. Interestingly, when n = 1/p, we have:

1 – (1 – p)ⁿ
= 1 – (1 – 1/n)ⁿ
→ 1 – 1/e
≈ 63.2%

So interestingly as n goes to infinity we have a limit of success.

But increasing the number of trials does increase your chance of success. To get a 99 percent chance of success:

0.99 = 1 – (1 – 1/100)ⁿ
0.99ⁿ = 0.01
n = ln(0.01)/ln(0.99
n ≈ 458.2

Rounding up to the nearest 100, we would need 500 trials to get a 99 percent chance of success.

Leila Hormozi’s initial tweet was met with plenty of sarcasm and some name calling, even earning a “community note” to clarify the actual math. But she took the higher road and replied with the following tweet.

Community Note is right.
It’s ~63%, not 100%.

Somehow I’ve managed to function and become successful in business despite being atrociously bad at math. lol. not a secret you can ask my team.

Here’s what I meant to say:
1 attempt = 1% odds.
100 attempts = 63% odds.
500 attempts = 99.3% odds.

Persistence doesn’t guarantee success. It does compounds your probability until the math is eventually on your side.

And now we know that the worse you are at math…. the less time it takes🫣😂😅

Seeing a 99% failure rate, many people give up right away, and as the famous saying goes, you miss 100 percent of the shots you don’t take.

Some people will try for 100 times, but be disappointed by the 36.6% chance of failure.

But very few people will persist for 500 attempts and reap the high 99% chance of success.

The math of success is that failure is acceptable; but not trying is not acceptable. While luck will play a role, perhaps it is those ignorant of the odds who are happy to keep trying and will succeed against all odds.

References

Leila Hormozi
https://x.com/LeilaHormozi/status/2045498332928209202
https://x.com/LeilaHormozi/status/2046202486525211089

Zocchihedron Man, CC BY-SA 3.0
https://commons.wikimedia.org/wiki/File:Zocchihedron2.jpg

Math StackExchange
https://math.stackexchange.com/questions/165993/average-number-of-times-it-takes-for-something-to-happen-given-a-chance

Rober Mistake similar mistake years ago
https://x.com/MarkRober/status/1168950821570195456
http://mindyourdecisions.com/blog/2019/09/23/puzzle-inspired-by-mark-rober-tweet/

Sandra was asked her age. She answered:

80 – 40÷10×4

How old is Sandra?

As usual, watch the video for a solution.

What this viral math problem taught me about the order of operations

Or keep reading.

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Answer To How Old Is Sandra?

(Pretty much all posts are transcribed quickly after I make the videos for them–please let me know if there are any typos/errors and I will correct them, thanks).

80 – 40÷10×4 = ?

The correct answer is 64 according to the modern interpretation of the order of operations.

But it is possible Sandra is 79, or some other age, and is just happy to troll the internet. As they say, never ask a woman her age!

With that said, it is important for students to understand the order of operations.

The order of operations

The expression can be simplified by the order of operations, often remembered by the acronyms PEMDAS/BODMAS.

First evaluate Parentheses/Brackets, then evaluate Exponents/Orders, then evaluate Multiplication-Division, and finally evaluate Addition-Subtraction. If two operations of the same precedence appear, evaluate from left to right.

According to the order of operations, division and multiplication have the same precedence, so the correct order is to evaluate from left to right.

First take 40 and divide it by 10, and then multiply by 4. Finally subtract that from 80

80 – 40÷10×4
= 80 – (40÷10)×4
= 80 – 4×4
= 80 – 16
= 64

This is without a doubt the correct answer according to the modern interpretation of the order of operations.

But some people may have learned it a different way.

The other result of 79

Historically the symbol ÷ was used to mean you should divide by the entire product on the right of the symbol (see longer explanation below). In other words you need to do the multiplications first and then the division.

Under that interpretation:

80 – 40÷10×4
= 80 – 40÷(10×4)
(Important: this is outdated usage!)
= 80 – 40÷40
= 80 – 1
= 79

This gives the result of 79. This is not the correct answer that calculators will evaluate; rather it is what someone might have interpreted the expression according to older usage.

Here’s a textbook from 1969 sent to me by Pete P.

1969 Textbook Mathematics for Management and Finance, with Basic and Modern Algebra 2nd Ed., Stephen P. Shao, Ph. D. Professor of Management and Statistics, School of Business Administration, Old Dominion University.

So if some people learned it one way, and other people learned it another way, is there really any saying what the correct answer is?

Calculators and coding languages are unanimous

If you input this expression into Python, Java, Excel, or any cell phone calculator you will get:

40÷10×4 = 16

If the 2 conventions really were equally valid, then evidently the people who learned 40÷10×4 = 1 were not employed by tech companies that made calculators.

I think this is strong evidence there is a left to right preference, consistent with what is taught in schools today (at least in America). So I would say:

80 – 40÷10×4 = 64

But perhaps Sandra actually is 79 years old, wanted to obfuscate her age (never ask a woman her age!), and was happy to troll the internet with the other convention that she learned in school.

However, I do think it’s important to learn what calculators and programming languages will interpret this expression. The day may come where you have to review someone’s code, and you better know how computers parse this expression!

*Note: I get many, many emails arguing with me about these order of operations problems, and most of the time people have misunderstood my point, not read the post fully, or not read the sources. If you send an email on this problem, I may not have time to reply.

References

Chicago History on X
https://x.com/Chicago_History/status/2052495811259347085

Lennes, N. J. “Discussions: Relating to the Order of Operations in Algebra.” The American Mathematical Monthly 24.2 (1917): 93-95. Web. http://www.jstor.org/stable/2972726?seq=1#page_scan_tab_contents

Christman, John Michael. Shop Mathematics. United States, Macmillan, 1922. Page 4.
https://www.google.com/books/edition/Shop_Mathematics/42wXAAAAYAAJ?hl=en&gbpv=1&dq=%22use+parentheses%22+division+symbol&pg=PA4&printsec=frontcover

As usual, watch the video for a solution.

How Tall Is The Dog Puzzle?

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Answer To How Tall Is The Dog Puzzle?

(Pretty much all posts are transcribed quickly after I make the videos for them–please let me know if there are any typos/errors and I will correct them, thanks).

Method 1: Algebra

Let p be the height of the post, and d be the height of the dog. From the diagram we have:

200 + d = p
p + d = 300

Substituting the first equation for p into the second gives:

200 + d + d = 300
200 + 2d = 300
2d = 100
d = 50 cm

Method 2: Visual Dog

Overlapping the two images of the dog will eliminate the dog variable to give the diagram:

We now have:

2p = 300 + 200
p = 250

Using the right diagram in the original figure we have:

p + d = 300

Since p = 250, we must have d = 50 cm.

Method 3: Visual Pole

We can alternately overlap the images of the poles to eliminate the pole variable:

We thus have:

d + 200 + d = 300
2d + 200 = 300
2d = 100
d = 50

Reference

https://x.com/codek_tv/status/2037414684484321603