Question

When rolling a 6-sided die, what's the probability of having to roll 6 times before you get a 4?

I'm trying to use binomial and geometric functions here.

Answer 1

at least six times?

Answer 2

Since this doesn't have a set number of trials, it's a geometric distribution.

Answer 3

or exactly six times?

Answer 4

@mhchen Yeah I figured that much out.

Answer 5

@satellite73 Exactly 6 times

Answer 6

######4 is what you want

Answer 7

where # means a number besides 4

Answer 8

Ok first you have to fraction out the possibility of rolling on that number

Answer 9

So the success is 1/6 ofc

And for the geometric formula at P(X=6) is \[p(1-p)^{n-1}\]

Since it's 5 failures and 1 success on the 5th trial.

So then you plug in the numbers
\[(\frac{1}{6})(1-\frac{1}{6})^{6-1}\]

Answer 10

Sorry I meant *6th trial

Answer 11

Geocdf?

Answer 12

I got 0.067

Answer 13

interesting, because i never know the names of these distributions
not 6, not 6, not 6, not 6, not 6, 6\[\left(\frac{5}{6}\right)^5\times \frac{1}{6}\]

Answer 14

(5/6)^6 * (1/6) = 0.056

Answer 15

it keeps you from writing silly stuff like \[(1-\frac{1}{6})\]

Answer 16

Yeah, same here, about 0.067ish

Answer 17

I'm not really a 'logical thinker' :b

I rely more on formulas

Answer 18

Yeah same here. That's why I was wanting to know what goemetric function it uses. I don't need to know the formulas.