How do I do the highlighted part of this question?

[analog jetty]

1. Wait patiently for a helper to come along.
2. Once someone helps you, say thank you and close the thread with:

+close

3. Feel free to nominate the person for helper of the week in #helper-nominations
4. Do not ping the mods, unless someone is breaking the rules.
5. If you're happy with the help you got here, and the server overall, you can contribute financially as well:

[distant haven]

Use the binomial distribution.
Also, considering that the number of successes for this event is a lot larger than the number of failures, it will be quicker to go from the opposite event.

[bright comet]

how do i use the binomial distribution

[distant haven]

Suppose we have n events, each having probability of success p.
Then the number of successes X follows a binomial distribution: X ~ Bin(n, p).
The PMF of X then is p(k) = C(n, k)p^k (1 - p)^(n - k), where C(n, k) = n!/(k! (n - k)!) is the binomial coefficient (number of combinations).

[bright comet]

ah thank you, so putting n as 5 and p as 1/5 would give us the answer?

[outer depot]

@bright comet has given 1 rep to @distant haven

[distant haven]

No.

[distant haven]

Well, we have 28 spins, so n = 28. p = 1/5, that's correct.
Our event is X ≥ 7, so it has 22 outcomes. Note, however, that the opposite event only has 7 outcomes. So, it will be quicker to calculate its probability first.

[bright comet]

why 22 outcomes?

[distant haven]

There are 22 integers from 7 to 28.

[bright comet]

ah

[bright comet]

wait but why is one faster than the other if you just plug numbers into a formula

[distant haven]

Because in case of our event there will be 22 terms, but in case of the opposite event - only 7 terms.

[bright comet]

so it's easier to do it the other way if you're not using a calculator?

[distant haven]

Yes.
Besides, sometimes the number of outcomes of an event is infinite, but finite for the opposite event. Then it's pretty obvious that it's easier to work with the opposite event first.

[bright comet]

ah got it ty

[outer depot]

@bright comet has given 1 rep to @distant haven