Percentage Of Rolling A Six On A Die 3 Times In A Row?

[Zacs-Master]

Question Details Here

[Jackdaw33]

1/216

[waterboatman]

1 in 6

[Tilly2]

5%?

[Buenchico]

1/6 x 1/6 x 1/6 = 1/216 = 100/216% = 0.463% (to 3 s.f.)

[Jackdaw33]

0.005%

3 times in a row must equate to 1/6 x 1/6 x 1/6.

[Peter Pedant]

more like 0.5%

whatever 100 /216 is as a decimal

[Buenchico]

JD33:

The probability (to 1 s.f) is, indeed, 0.005 but you need to multiply that by a hundred to convert it to a percentage, giving 0.5% (to 1 s.f.)

[Jackdaw33]

Some queer mathematicians here tonight.

[waterboatman]

Every time you roll the dice it is 1 in 6.

[Jackdaw33]

That is not the question, WB.

[Buenchico]

Agreed, Boaty.

If the question was "What's the probability of getting a 6 after already getting six on the two previous goes?" then the answer would, indeed, be 1/6.

However the question isn't that. It's simply "What's the probability of getting three sixes in a row?", so 1/6 needs to be cubed.

[TheChair]

//Every time you roll the dice it is 1 in 6.//
True, but the question is not "If you have rolled 2 sixes, what is the chance of rolling another?" (to which the answer would indeed be 1/6), but "what is the chance of rolling 3 sixes in a row?"

[waterboatman]

The odds are the same however many times you roll the dice. Six sides. 1 in 6.

[TheChair]

Buenchico can type faster than me, even when his answer is longer.

[TheChair]

//The odds are the same however many times you roll the dice.//

The odds are the same *for each roll of the dice", but we are concerned with the *combined* odds of 3 consecutive rolls of the dice.

[waterboatman]

Evening Chris. Mathematicians, statisticians and engineers will never agree on such a question mate.

[waterboatman]

TC it's still 1 in 6 (I'm a retired engineer by the way) ;-)

[Buenchico]

I think they will, Boaty!

As a graduate mathematician (with a specialism in statistics for my degree) who's written the section on probability for a textbook which is still in use in schools (as well as teaching the subject to CSE, O-level, GCSE and A-level), I'm reasonably confident about my answer ;-)

[fiction-factory]

How can it be 1 in 6, WBM?