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# S1 jan 2009 question 8 watch

1. A game uses an unbiased die with faces numbered 1 to 6. The die is thrown once. If it shows 4 or 5 or
6 then this number is the final score. If it shows 1 or 2 or 3 then the die is thrown again and the final
score is the sum of the numbers shown on the two throws.
(i) Find the probability that the final score is 4.

Confused why the answer is

1/6 + 3*(1/6)^2

I would have thought the answer was:
1/6 + 4*(1/6)^2
Because u can have
a 4 (1,3)(3,1)(2,2)(2,2)
2. (Original post by ineedhelpwithph)
A game uses an unbiased die with faces numbered 1 to 6. The die is thrown once. If it shows 4 or 5 or
6 then this number is the final score. If it shows 1 or 2 or 3 then the die is thrown again and the final
score is the sum of the numbers shown on the two throws.
(i) Find the probability that the final score is 4.

Confused why the answer is

1/6 + 3*(1/6)^2

I would have thought the answer was:
1/6 + 4*(1/6)^2
Because u can have
a 4 (1,3)(3,1)(2,2)(2,2)
You put (2,2) twice.
3. (2,2) is the same you don't count it twice. It's not the same as (1,3) and (3,1) because the order matters since it makes a difference as you either get a one first or three whereas if you score a two both times it's the same.
4. (Original post by Han-Mingi)
(2,2) is the same you don't count it twice. It's not the same as (1,3) and (3,1) because the order matters since it makes a difference as you either get a one first or three whereas if you score a two both times it's the same.
Thanks just wondering because there are 2 possible ways to get 2,2 how come you don't count it twice?
5. (Original post by ineedhelpwithph)
Thanks just wondering because there are 2 possible ways to get 2,2 how come you don't count it twice?
Your list was 4(1,3)(3,1)(2,2)(2,2) but you see getting (2,2) is the same as the first time. It's not the same as getting (1,3) and (3,1), Why? You ask. Well just take a look at the number order it's different but with your (2,2) and (2,2) it's the same so you can't count (2,2) twice. It's like saying give me using all 1,2,3 all the possible combinations to add to four, well there's 1+3, 3+1, 2+2, 2 is the same as 2 but 1 does not equal
3 hence you can swap the order for 1 and 3 but not for 2+2 because it's the same

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