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Thanks for the detailed response! On a quick look, for the second (bus/plane) example, it appears you didn't use the binomial distribution formulas for this?

Thanks for the detailed response! On a quick look, for the second (bus/plane) example, it appears you didn't use the binomial distribution formulas for this? Is there a name I could google for the formulas you used ? edit: I'm puzzled by the fact that the probability term was RAISED to the number of hours, rather then multiplied by it? so the chance isn't linear with the amount of time ? Thanks!

stncls 5y ago
> it appears you didn't use the binomial distribution formulas for this You would use binomial distribution formulas if the problem was more complex. Say, if you cared about how many times you get covid infected, or how many times your winning ticket is drawn. The problem here is a special, simpler case. > Is there a name I could google for the formulas you used ? Any intro to probabilities book will start with such problems. If you really want to google something, the basic assumption here is that the events are "independents". You can find examples here: https://en.wikipedia.org/wiki/Independence_(probability_theory)#Examples https://en.wikipedia.org/wiki/Independence_(probability_theo...
- mech422 5y ago
  Thanks! I appreciate the links/google fodder - it'll let me RTFM more on this stuff...
stncls 5y ago
> I'm puzzled by the fact that the probability term was RAISED to the number of hours, rather then multiplied by it? so the chance isn't linear with the amount of time ? Yes it is not linear. Imagine you are repeatedly throwing a dice. The probability that you get a "6" at some point is absolutely not linear with the number of throws: P(not a single "6" in N throws) = (4/5)^N so P(at least one "6" in N throws) = 1 - (4/5)^N Edit: Also, raw probabilities are constrained to the interval [0, 1]. So they are rarely linear in a parameter, because, then, they would easily escape the [0, 1] interval. Imagine that we had P(covid) = some_constant * some_parameter. There would be values of the parameter such that P(covid) > 1, which does not make sense.
- mech422 5y ago
  Thanks! This will probably make more sense once I can RTFM the probability stuff..

stncls 5y ago

> it appears you didn't use the binomial distribution formulas for this You would use binomial distribution formulas if the problem was more complex. Say, if you cared about how many times you get covid infected, or how many times your winning ticket is drawn. The problem here is a special, simpler case. > Is there a name I could google for the formulas you used ? Any intro to probabilities book will start with such problems. If you really want to google something, the basic assumption here is that the events are "independents". You can find examples here: https://en.wikipedia.org/wiki/Independence_(probability_theory)#Examples https://en.wikipedia.org/wiki/Independence_(probability_theo...

mech422 5y ago
Thanks! I appreciate the links/google fodder - it'll let me RTFM more on this stuff...

stncls 5y ago

> I'm puzzled by the fact that the probability term was RAISED to the number of hours, rather then multiplied by it? so the chance isn't linear with the amount of time ? Yes it is not linear. Imagine you are repeatedly throwing a dice. The probability that you get a "6" at some point is absolutely not linear with the number of throws: P(not a single "6" in N throws) = (4/5)^N so P(at least one "6" in N throws) = 1 - (4/5)^N Edit: Also, raw probabilities are constrained to the interval [0, 1]. So they are rarely linear in a parameter, because, then, they would easily escape the [0, 1] interval. Imagine that we had P(covid) = some_constant * some_parameter. There would be values of the parameter such that P(covid) > 1, which does not make sense.

mech422 5y ago
Thanks! This will probably make more sense once I can RTFM the probability stuff..