Given Probability Problem does not work if Greg's alternative approach is used

[user3109]

For the Given Probability PrepSwift video, Greg demonstrates that in a “given” probability problem, you can use the probability OR the number of the permutations of cases.

For example, for Case 3 and Case 4 of the screenshot, I should be able to calculate:

Case 3: 4! / (2!)(2!) = 6
Case 4: 4! / 3! = 4
Case 5: 4! / 4! = 1

Then I put Case 5 / All → 1 / 11

This is not the right answer. Thus, the number of cases alternative approach should not be used? Please help!

Update: I tried using this case permutations method on subsequent problems, and it appears it only works SOMETIMES. Weird!

[cylverixxx]

@user3109

Case 3: 4! / (2!)(2!) = 6
Case 4: 4! / 3! = 4
Case 5: 4! / 4! = 1

That’s the number of arrangements. For each arrangement, there’s a corresponding probability of occurring, so not every element in the sample space is equiprobable.

@user3109

Then I put Case 5 / All → 1 / 11

You’re assuming each element in the sample space is equiprobable right here^^

[user3109]

Thank you this makes sense!!