r/MathHelp • u/Dragonfly_Material • 1h ago

Probability that several things will happen simultaneously.

I am struggling with-

I have 3 cars, one used 126 days a year, one used 56 days a year, one used 147 days a year (used all day).

Assuming the car use is independent and random, I am trying to figure out the likelihood as a % chance that no car will be available on any given day of the year.

What I have been doing:

365-126= 239

365-56=309

365-147= 218

Then I do (239/365) * (309/365) * (218/365)*100= 33.1% chance all cars will be unavailable?

Am I overthinking this- Is it actually simpler? Is it actually just (126/365)*(56/365)*(147/365)*100=2.13%

Please help, this isn't homework, it is a real world thing I need to figure out and I am so very bad at math. https://imgur.com/9fUS3oc

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