# Math Probabilities Qn

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#### vince123123

##### Guest
need to enlist the aid of those who still can remmeber probabilities....i returned all to the teacher years ago

anyway the qn is, if i throw three dice, whats the probability that at least ONE of them will show a certain number that i picked. e.g. i pick number 6. whats the probability that at least ONE of them will show a 6?

b) how about 2 of them?

hope to get some answers! cheers!

#### mpenza

##### Senior Member
a) 1/6+1/6+1/6 = 1/2

taking b to mean three dice thrown, two giving the same number selected.
b) 1/6*1/6+1/6*1/6+1/6*1/6 = 1/12

might be a bit wrong though due to some overlap.

#### mpenza

##### Senior Member
try again:

b) 1/6*1/6*5/6+1/6*1/6*5/6+1/6*1/6*5/6+1/6*1/6*1/6=0.074074

a) 1/6*5/6*5/6+1/6*5/6*5/6+1/6*5/6*5/6+ b = 0.4213

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#### vince123123

##### Guest
hehe i initially thot the answer was 1/2 also in (a). but i realised that it can't be, cos if using that working, throwing 6 dice gives a probability of 1 to get the number

mpenza said:
a) 1/6+1/6+1/6 = 1/2

taking b to mean three dice thrown, two giving the same number selected.
b) 1/6*1/6+1/6*1/6+1/6*1/6 = 1/12

might be a bit wrong though due to some overlap.

#### ST1100

##### Senior Member
Use counting methods instead of probability. Sure correct one.

3 dice gives 6x6x6 = 216 possible combinations (use a spreadsheet if you need). Out of these 216, 91 combinations contain the number 6. Therefore, the answer is 91/216.

1/2 is the wrong answer bcoz it does not take overlapping solutions into account.

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#### vince123123

##### Guest
wah how did you figure that out so fast? how u get the ez way to come up with all the combos?

ST1100 said:
Use counting methods instead of probability. Sure correct one.

3 dice gives 6x6x6 = 216 possible combinations (use a spreadsheet if you need). Out of these 216, 91 combinations contain the number 6. Therefore, the answer is 96/216.

1/2 is the wrong answer bcoz it does not take overlapping solutions into account.

#### mpenza

##### Senior Member
ST1100 said:
Use counting methods instead of probability. Sure correct one.

3 dice gives 6x6x6 = 216 possible combinations (use a spreadsheet if you need). Out of these 216, 91 combinations contain the number 6. Therefore, the answer is 96/216.

1/2 is the wrong answer bcoz it does not take overlapping solutions into account.
same answer as mine ;p yup, working out the combinations is a sure way to get the answer but it might be quite tedious for cases which have a lot more combinations.

#### ST1100

##### Senior Member
vince123123 said:
wah how did you figure that out so fast? how u get the ez way to come up with all the combos?
Erm, i did it mentally, but for 2 or more numbers, i would use a spreadsheet:

1 1 1
1 1 2
1 1 3
1 1 4
...
...
6 6 3
6 6 4
6 6 5
6 6 6

If you know some excel programming, you can get excel to do the counting for you too.

(Actually, i'm still trying to think of a correct way to calculate this using probablity instead of counting.)

#### ST1100

##### Senior Member
Ok, the way to do it with probabilities:

There is a 5/6 chance that there is no 6 on the first dice, and 5/6 chance on the second and third. Therefore, the answer is 1-(5/6^3).

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#### vince123123

##### Guest
wah not bad, so far there are 3 diff workings and all get hte same answer

thanks guys!

#### mpenza

##### Senior Member
this is a faster than what I've calculated ;p

#### romeo

##### New Member
wahh.. probability.. did that last time ... for statistics classes...

#### simplicity_

##### New Member
Well done! As an ex-Statistics major, for a while I did not know how and where to start! :embrass:
tsk tsk. :nono: hahah, return all to teacher liao ar? :bsmilie:

#### romeo

##### New Member
No ... I am a teacher who has lost it! :bsmilie:
even worst... :bsmilie:

heehee.. :bsmilie:

Btw... you graduated with a degree in statistics?

#### simplicity_

##### New Member
No ... I am a teacher who has lost it! :bsmilie:
hahaha..

:kok: haiyoh.. jia lat leh, liddat. :bsmilie:

#### di0nysus

##### New Member
visualise a tree diagram,...each die giving off to 6 branches, it'll be easy.

ST1100's answer using P(an event) = 1 - P(all other events) = 1-(5/6^3) is the quickest.

#### ST1100

##### Senior Member
BTW, the answer for picking two numbers is 1-(4/6 ^3).

Generic formula is 1-((6-r)/6 ^ d), where r is the number of picks and d the number of dice.

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