Question

What is the probability that three standard dice rolled simultaneously will all land with the same number facing up?

Answer 1

Reqd. Prob.`=6/216=1/36`.

Explanation:

let us denote by, `(l,m.n)` an outcome that the nos. `l,m,n` appear on the face of the first, second and third die, resp.

To enumerate the total no. of outcomes of the random experiment of rolling `3` std. dice simultaneously, we note that each of l,m,n can take any value from {1,2,3,4,5,6}

So, total no. of outcomes`=6xx6xx6=216`.

Among these, no. of the outcomes favorable to the given event is `6`, namely, `(1,1,1), (2,2,2), (3,3,3), (4,4,4), (5,5,5) and (6,6,6)`.

Hence, the Reqd. Prob.`=6/216=1/36`.

Answer 2

`1/36`

Explanation:

In probability questions it is very confusing to think through what is happening if things all happen at the same time! It really does not matter if 3 dice are rolled simultaneously, or one after the other.

Throw the first die.... There are 6 different possible outcomes, any will do.

But whatever number shows is the number we want to get on the second and third dice.

SO for the next two throws we are limited to only ONE of the possible outcomes:

P (same number) =`6/6 xx1/6 xx1/6 = 6/216`

=`1/36`