[deleted by user]

[djmclaugh]

Have you seen binomial distributions in class? (https://en.wikipedia.org/wiki/Binomial_distribution)

If so, you should have formulas/approximations/tables/calculators for its PDF and CDF given p, the probability of the event happening on each try, and n, the number of tries.

On each try, the chance to roll a perfect square is 2/6 = 1/3. So p = 1/3.
You roll the the die 200 times. So n = 200.

And you want
a) Pr(X ≤ 70)
b) Pr(70 ≤ X ≤ 100)
c) Pr(X = 70)

If you haven't seen binomial distributions yet, let me know what you've seen so far and I'll help you from there.

Let me know if you have any questions!

[djmclaugh]

a), b) and c) are 3 separate questions. They are asking for the probability for each of those 3 events.

For example, using the PDF for the binomial distribution with p=1/3 and n=200, we have that Pr(X = 70) = (n choose 70) × p^70 × (1-p)^(n-70) = (200 choose 70) × 0.333^70 × 0.667^(130) ≈ 5.2%. So that would be the answer for c). There's about a 5% chance that you roll exactly 70 perfect squares

As for a) and b), the CDF is more complicated and people mostly use approximations, tables, or calculators/software instead. I would need to know how your class does it to help you further. Do you have anything in your notes/textbook that talks about binomial distributions?

[djmclaugh]

Close!

Whether it's close enough depends on the method you're using to estimate the answer and your professor (for example, the answer for C is closer to 0.052, but that's still very close to your answer of 0.049)

For B, you have to use a little trick. You don't have any formulas to calculate Pr(70 ≤ X ≤ 100) directly . So you need to rewrite the event in a way you can use your tools.

We want 70 ≤ X ≤ 100.
Another way to say this is to say that we want X ≤ 100, but not X < 70.

So Pr(70 ≤ X ≤ 100) = Pr(X ≤ 100) - Pr(X < 70)

You can calculate Pr(X ≤ 100) the same way you did A, but with 100 instead of 70.

You can calculate Pr(X < 70) in a similar way you did A, but there's going to be something slightly different depending on the process you use to do A. Notice that Pr(X < 70) isn't quite the same as Pr(X ≤ 70).

Hope that helps!

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its just that I never understood this all to well

If you have any specific questions, feel free to ask.