Average Roll

[BonJoviJones]

Roll a die. If you roll a 6, roll again. Repeat until you don't roll a six. Your score is the sum of all rolls.

What is the average score in this game?

[kyro]

(1/6)(1+2+3+4+5) + (1/6)(6) + (1/6)(1/6)(1+2+3+4+5)+ (1/6)(1/6)(6) + (1/6)(1/6)(1/6)(1+2+3+4+5) + ...

15/6 + 1 + 15/36 + 1/6 + 15/216

15/6(1 + 1/6 + 1/36 + ... 1/6^n) + 1(1 + 1/6 + 1/36 + ... + 1/6^n)

(15/6)(6/5) + (1)(6/5)

3 + 1.2

4.2

I think, someone correct me if I'm wrong.

[BruceZ]

[ QUOTE ]
(1/6)(1+2+3+4+5) + (1/6)(6) + (1/6)(1/6)(1+2+3+4+5)+ (1/6)(1/6)(6) + (1/6)(1/6)(1/6)(1+2+3+4+5) + ...

15/6 + 1 + 15/36 + 1/6 + 15/216

15/6(1 + 1/6 + 1/36 + ... 1/6^n) + 1(1 + 1/6 + 1/36 + ... + 1/6^n)

(15/6)(6/5) + (1)(6/5)

3 + 1.2

4.2

I think, someone correct me if I'm wrong.

[/ QUOTE ]

Right. Or you could just note that since the probability of not rolling a 6 is 5/6, it will take an average of 6/5 rolls to not roll one, and the average score per roll is 3.5. Then 3.5 * 6/5 = 4.2.

[gaming_mouse]

[ QUOTE ]

Right. Or you could just note that since the probability of not rolling a 6 is 5/6, it will take an average of 6/5 rolls to not roll one, and the average score per roll is 3.5. Then 3.5 * 6/5 = 4.2.

[/ QUOTE ]

Clever.

[kyro]

i have no idea what you just did. i'm going to spend my night figuring that out.