Simulation Probability

[a weaponized ikea chair]

Hey,

Here's the question:

A teacher gives the class a test consisting of 10 multiple-choice questions, each with five alternatives. Use simulation to estimate the probability that a student who guesses the answer to every question gets at least five correct.

I do not understand how you are supposed to work out the answer, or how they got to the answer of approx 0.0009.

Any help appreciated.

[jammol7]

Idk I suck at probability but I keep getting 0.032 as my answer. I'm using the nCr thing on the CAS and just adding all the probabilities together. I'm probably doing something wrong.

[a weaponized ikea chair]

Idk I suck at probability but I keep getting 0.032 as my answer. I'm using the nCr thing on the CAS and just adding all the probabilities together. I'm probably doing something wrong.

yeah that's what I got but it says the answer is approx 0.0009

[jammol7]

yeah that's what I got but it says the answer is approx 0.0009

um that's weird.

I did nCr(10,5) * (0.2)⁵ * (0.8)⁵ + nCr (10,6) * 0.2⁶ * (0.8)⁴ ... until nCr(10,10) and the answer I get is 0.03202.

I also tried through doing no. of correct possibilities / total no. of possibilities, it's 312689/9765625 which is 0.03201935...

I'm gonna say the answer might be wrong?

[Sine]

Yeah seems like that answer is way too low. Even just the probability of getting 5/10 is higher than that.

[jammol7]

Yeah seems like that answer is way too low. Even just the probability of getting 5/10 is higher than that.

oh yeah true. Probability of getting exactly 5/10 is 0.026 haha.

[a weaponized ikea chair]

Thanks all for your answers

[darkz]

um that's weird.

I did nCr(10,5) * (0.2)⁵ * (0.⁵ + nCr (10,6) * 0.2⁶ * (0.⁴ ... until nCr(10,10) and the answer I get is 0.03202.

I also tried through doing no. of correct possibilities / total no. of possibilities, it's 312689/9765625 which is 0.03201935...

I'm gonna say the answer might be wrong?

Btw, just a tip, if you're using the tinspire, you can use the binomCdf function instead of adding up all the individual probabilities.

[jammol7]

Btw, just a tip, if you're using the tinspire, you can use the binomCdf function instead of adding up all the individual probabilities.

damn, that makes it so much easier. thanks mate.

should I be concerned about getting slightly different answers though? When I add them up individually using the nCr command I get 0.03201 but when I use binomCdf I get 0.03279. Seems too big to be a rounding error?

[darkz]

damn, that makes it so much easier. thanks mate.

should I be concerned about getting slightly different answers though? When I add them up individually using the nCr command I get 0.03201 but when I use binomCdf I get 0.03279. Seems too big to be a rounding error?

Well I did it your way and I got the right answer - so I'd assume that you either incorrectly typed something, or you did each probability separately (perhaps float to less decimal points) and then added them up? Using the binom function is the safest.

[jammol7]

Well I did it your way and I got the right answer - so I'd assume that you either incorrectly typed something, or you did each probability separately (perhaps float to less decimal points) and then added them up? Using the binom function is the safest.

ah thanks. I tried it again and got the right answer. Probably a rounding error from me only adding the first couple of decimal places.