# Probability with a dice

• Mar 31st 2013, 02:34 PM
Paze
Probability with a dice
I throw a dice 6 times. What are the odds of getting higher than 4 on at least 5 throws?

Can I write this as: $\displaystyle \left(\frac{2}{6}\right)^5+\frac{2}{6}$ ?

In other words..The odds of getting a 5 or 6, 5 times in a row..Plus the probability of getting it in the 6th throw?
• Mar 31st 2013, 02:48 PM
HallsofIvy
Re: Probability with a dice
So getting higher than 4 on 5 or 6 throws? Yes, the probability of getting 5 or 6 on one through is 2/6= 1/3 so the probability of throwing 5 or 6 6 consecutive times is $\displaystyle (1/3)^6$. The probabilty of get 5 or 6 exactly 5 times is $\displaystyle 6(1/3)^5(2/3)$. The probabilty of either of those happening is the sum, $\displaystyle (1/3)^6+ 6(1/3)^5$.

Notice the "6" in that? That is because there are 6 different orders: YYYYYN, YYYYNY, YYYNYY, YYNYYY, YNYYYY, and NYYYY where "Y" means a 5 or 6 and "N" means not a 5 or 6.

(And, by the way, the word "dices" is a verb meaning "cuts something into small cubes". The word you want is "dice" which is itself the plural of the word "die".)
• Mar 31st 2013, 03:08 PM
IMTinstructor
Re: Probability with a dice
Hi:

You want to use the binomial distribution for this problem. Are you familiar with that distribution?

Howard Heller
InteractiveMathTutor.com
• Mar 31st 2013, 03:09 PM
Plato
Re: Probability with a dice
Quote:

Originally Posted by Paze
I throw a dice 6 times. What are the odds of getting higher than 4 on at least 5 throws?
Can I write this as: $\displaystyle \left(\frac{2}{6}\right)^5+\frac{2}{6}$ ?
In other words..The odds of getting a 5 or 6, 5 times in a row..Plus the probability of getting it in the 6th throw?

I think that there is a language(translation) difficulty here.

First I do not like the word odds and never use it. So I change it to probability.

Thus "What are the probability of getting higher than 4 on at least 5 throws?"
That means "getting a five or six at least five times out of six throws".

If you agree that is what it means, then the answer is:
$\displaystyle \binom{6}{5}\left( {\frac{2}{6}} \right)^5}\left( {\frac{4}{6}} \right) + {\left( {\frac{2}{6}} \right)^6$
• Mar 31st 2013, 03:19 PM
IMTinstructor
Re: Probability with a dice
That is correct now.

Howard Heller
InteractiveMathTutor.com
• Mar 31st 2013, 03:45 PM
Plato
Re: Probability with a dice
Quote:

Originally Posted by IMTinstructor
That is correct now.

Howard Heller
InteractiveMathTutor.com

Someone of your low IQ would not know if that is correct or not.
Anyone stupid enough to fall for you scam deserves the outcome.
I can find no entry for you at MathGenealogy Project

So what equips you to tutor?
• Mar 31st 2013, 04:12 PM
IMTinstructor
Re: Probability with a dice
Math major, math expert, actuarial science major, MBA
• Mar 31st 2013, 04:35 PM
Plato
Re: Probability with a dice
Quote:

Originally Posted by IMTinstructor
Math major, math expert, actuarial science major, MBA

Oh my goodness. Do you really think that has anything to do with mathematics?
What does "Math major" mean? "actuarial science major" has very little to do with mathematics.

I live in a state in which it is illegal to call oneself a "blank" if one does not have a PhD in "blank".
I can thank my brother for that, "educational psychologist is not a psychologist".

Do you have a PhD?
• Mar 31st 2013, 05:03 PM
Paze
Re: Probability with a dice
Thanks guys. This helped me understand my problem! On to the next...
• Mar 31st 2013, 05:05 PM
Paze
Re: Probability with a dice
Quote:

Originally Posted by Plato
I think that there is a language(translation) difficulty here.

First I do not like the word odds and never use it. So I change it to probability.

Thus "What are the probability of getting higher than 4 on at least 5 throws?"
That means "getting a five or six at least five times out of six throws".

If you agree that is what it means, then the answer is:
$\displaystyle \binom{6}{5}\left( {\frac{2}{6}} \right)^5}\left( {\frac{4}{6}} \right) + {\left( {\frac{2}{6}} \right)^6$

Or wait, hold on. Your answers differs from Halls's answer, doesn't it? I got the same answer as HallsOfIvy. Where does the 4/6 come from?