Probability (attachment)

[Jefferson]

Could I have some help with part (c) and (d)?
See Attachment.

Answers:

(a) 1/2 * 1/2 * 1/6 * 1/6 = 1/144 (confirmed)
(b) 1/2 * 1/2 * 5/6 * 1/6 = 5/144 (confirmed)

(c) To make 13 points:  Can be 5, 5, 3 (arranged in 3 different ways) or 5, 4, 4 (arranged 3 ways)
i.e.

(1/144 * 1/144 * 5/144 * 3) + (1/144 * 1/144 * 1/144 * 3) = 1/165888

TEXTBOOK ANSWER: 7/995328
(my answer is technically 6/995328. What did I miss :C?)

(d) Not sure what the quickest approach is (or any at all) to get their answer.
I did:
either 5,5,5 or 5,5,4 (to beat 13, assuming that's what they meant)
P(5,5,5 or 5,5,4 points) = (1/144 * 1/144 * 1/144) + (1/144 * 1/144 * 1/144 * 3) = 1/746496

TEXTBOOK ANSWER: 3/144 (prob wrong this one)

If a short cut is possible using 3U, I would also like to know .
Thank you!

[RuiAce]

Sorry for missing this! I just had a look and with part c) I reckon it's just a bit of error in the wording. I think they actually intended to ask for at least 13 in three moves, which would then get you the 5-5-5 case and bump your probability up as required.

Their wording is quite cryptic and I haven't figured out what their intended goal is for part d) yet.

[Jefferson]

Sorry for missing this! I just had a look and with part c) I reckon it's just a bit of error in the wording. I think they actually intended to ask for at least 13 in three moves, which would then get you the 5-5-5 case and bump your probability up as required.

Their wording is quite cryptic and I haven't figured out what their intended goal is for part d) yet.

Thank you for replying!
At least 13 for part (c) would also include the 5-5-4 case along with 5-5-5, which shoots over their answer it seems.
The wording for this question is terribly written I supposed, but hopefully I didn't make any errors doing it by my interpretation.

Thanks again!

[RuiAce]

Thank you for replying!
At least 13 for part (c) would also include the 5-5-4 case along with 5-5-5, which shoots over their answer it seems.
The wording for this question is terribly written I supposed, but hopefully I didn't make any errors doing it by my interpretation.

Thanks again!

Oh oops I completely missed the 5-5-4! Honestly though given that I'd say your answer is correct regardless. I can't see any other way of making 13 using those numbers and your reasoning for 5-5-3 and 5-4-4 is convincing.

So I'd say that their textbook answer is wrong. Given this I feel part d) would probably be a waste of time, because who knows if it relied on their incorrect answer for part c). The textbook has had mistakes in the answers in the past as well.