Wikipedia:Reference desk/Archives/Mathematics/2016 August 27

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August 27

How to calculate odds on percentages

I know this must seem like a really basic question, but it's a long time since I left school, and I didn't do well in math(s) even then.

How do I calculate the chance of say a 90% chance of something happening, and then the same thing again. So 90% and then 90% chance again, how do I calculate the odds of both 90% chances failing or succeeding? Thanks in advance. 95.148.212.141 (talk) 14:29, 27 August 2016 (UTC)

You multiply: 0.90 × 0.90 = 0.81 or 81% chance of two 90% probability independent events occurring. The chance neither will occur is 0.10 × 0.10 = 0.01 or 1%. For the chance it will happen once out of two tries we must consider the two ways that can happen: 0.90 × 0.10 = 0.09 or 9% and 0.10 × 0.90 = 0.09 or 9% too. So that's 18%. And 81% + 1% + 18% = 100%, so it checks out.

This method gets rapidly more complex, say when figuring the chance of 17 out of 23 events occurring, so then we use formulas with factorials. If you are interested, we can explain those, too. Note that odds, like 2-to-1, are different. StuRat (talk) 14:58, 27 August 2016 (UTC)

And to get the probability of any number of independent events all happening, you multiply the separate probabilities.→81.155.111.70 (talk) 22:33, 27 August 2016 (UTC)

This may help understand why we multiply (or maybe just confuse more): Percent means per hundred so 90% = 90/100 = 0.90. Imagine 100 tries are made. You expect the first event to happen in 90% of 100 tries = 0.90 × 100 = 90 times. You expect the second event to also happen in 90% of those 90 cases. 90% of 90 is 0.90 × 90 = 81. Out of the 100 tries that is 81/100 = 81% = 0.81. Skipping the steps about 100 tries, we have calculated 0.90 × 0.90 = 0.81 = 81/100 = 81%. PrimeHunter (talk) 01:08, 30 August 2016 (UTC)

It is important to note that this simple solution rests on the independence of the events. Assume you have pulleys that can lift exactly 100kg, and break if you try to lift more. Assume that 90% of your infinite number of loads are 100kg or less. If you try to lift two separate loads, you chance of success is 81%. But if the pulley breaks on the first load, and you then try to lift the same load with a second pulley, your chance of success is 0%. --Stephan Schulz (talk) 07:40, 2 September 2016 (UTC)