So I Managed to Put This on an Exam...

[Mew King]

I am a teaching assistant for an undergraduate probability course.  My goal for this term was to throw in a question even tangentially related to Pokemon on a midterm.  That's because 3 years ago, I took a graduate probability course by the same professor (who is also my current research adviser).  He had us write a paper about how probability plays a role in your life.  A lot of people were writing about their research, but I wasn't involved in any at the time.  So I wrote a paper on Pokemon.  I even wrote a Matlab program to simulate a battle between a Blissey and a Giratina to show how the different probabilities affect who wins.  The professor still remembers it even now (because it's unique).

So that's why I wanted to include a Pokemon related question on an exam.  During the second midterm, I finally succeeded, though I realized I could have used more recognizable names, but I was too involved in X&Y to consider it.

Either way, I propose the question to you guys to see if you can solve it (and sorry if it's in the wrong section, but it is related to Pokemon).



Lysandre Labs produces 200 Holo Casters a day. Each manufactured Holo Caster coming off the assembly line is
deemed faulty with a probability 1/100 , independently of the other Holo Casters. What is the probability that no more
than 5 Holo Casters are deemed faulty during a given day?



I'm going to try to do others during the next two exams, but last time I tried to use actual Pokemon I was turned down during the first exam.  I really wanted to do a question on the voltage of Pikachu's thunderbolts.  Assuming they're IID, they should follow a Gaussian distribution and thus I can ask students to find the top percentage of Pikachu's thunderbolts given a mean (about 10kV according to the Japanese name of the attack) and a variance.

[Delicious_Scout]

Descriptive Statistics are one of my favourite subjects, as well as Inferences and Econometrics. In general, I like them a lot.

Hint: Binomials? Cases in which X occur? Read well as well, since it is not the same to ask for one time and to ask for at least one time something to occur.

[Awkward Squirtle]

Lysandre Labs produces 200 Holo Casters a day. Each manufactured Holo Caster coming off the assembly line is
deemed faulty with a probability 1/100 , independently of the other Holo Casters. What is the probability that no more
than 5 Holo Casters are deemed faulty during a given day?

OK, 1/100 is faulty, so the chance of 5 is 1/100^5, or 1/10,000,000,000
200 tests means 200/100^5

that's 2/100^4, or 0.00000002

Is that right? I feel like there's some equation for expectation or something I should be using, but I think my answer works.

[Mew King]

Descriptive Statistics are one of my favourite subjects, as well as Inferences and Econometrics. In general, I like them a lot.

Hint: Binomials? Cases in which X occur? Read well as well, since it is not the same to ask for one time and to ask for at least one time something to occur.

Yup.  The test was on the basics of discrete PMFs.  So we went over of course binomial and geometric.  We also did some stuff with joint PMFs.

OK, 1/100 is faulty, so the chance of 5 is 1/100^5, or 1/10,000,000,000
200 tests means 200/100^5

that's 2/100^4, or 0.00000002

Is that right? I feel like there's some equation for expectation or something I should be using, but I think my answer works.

The first part will work if you take five at random and say what's the probability that all five are broken.  You also have to consider the probability that the rest are not broken.  You also have to consider other things like which 5 out of the 200 are broken.  We want to consider all possible sets of 5 broken ones.

And remember, the question says up to 5.  So you got to consider the case of 0, 1, 2, 3, and 4 are broken as well

[Sebastian Moran]

meanwhile i'm just sitting here kind of alarmed because i misread "holo casters" as "holocausters". 
 

[SirBlaziken]

Hm.... something to think about, that's for sure.

However, for being able to sneak in a pokemon related question onto a test, genius!

[Awkward Squirtle]

The first part will work if you take five at random and say what's the probability that all five are broken.  You also have to consider the probability that the rest are not broken.  You also have to consider other things like which 5 out of the 200 are broken.  We want to consider all possible sets of 5 broken ones.

And remember, the question says up to 5.  So you got to consider the case of 0, 1, 2, 3, and 4 are broken as well

Ah well, not done probability distributions since last year, wasn't great at them then tbh.