probability: Assume fair 6-sided die rolled 6 times....

[mathdweeb]

Small problem with a probability question.

Assume a fair and 6 sided die is rolled 6 times
How many possible outcomes are there for the event `precisely 2 numbers are bigger
than 4'? What is the probability of that event?

When i was going through it i solved it as follows :-

I said that the possible outcomes that were bigger than 4 would be 6^4 x 4
and that its probability is 6^4 x4 /6^6 which is equal to 1/9 ( however this is wrong) and im not sure what i did wrong :?:
help pliz.......

 

[tkhunny]

This is a Bernoulli experiment.

Pr(> 4) = Pr(5 or 6) = 1/3

With 6 attempts, it is now a Binomial experiment.

p = 1/3, q = 1-(1/3) = 2/3, n = 6

Let's see what you get.

 

[mathdweeb]

cheers for the tip
so i calculated it again as follows

[sub:19xl6xz1]6[/sub:19xl6xz1]C[sub:19xl6xz1]2[/sub:19xl6xz1]*(0.334)[sup:19xl6xz1]2[/sup:19xl6xz1]*(2/3)[sup:19xl6xz1]4[/sup:19xl6xz1]
= 0.331

does this look more rite?

 

[galactus]

Yep, that looks even gooder

 

[mathdweeb]

:lol:
cheers for the help