What is the probability of obtaining a sum of at least 5 when rolling a pair of dice?

Answer 1

There is a 1in 36 chance of rolling 2, a 2 in 36 chance of rolling 3 and a 3 in 36 chance of rolling 4. So there is a 30 in 36, or 5 in 6 chance of rolling at least 5 with a pair of fair dice.

------------------------------------------------------------

There is only 1 way of scoring 2 (1 and 1).

3 can be scored 2ways (1 & 3 and 3 & 1)

4 is possible 3 ways (1 & 3; 3 & 1; 2 & 2)

5 has 4 ways (1 & 4; 4 & 1; 2 & 3; 3 & 2)

6 has 5 ways (1 & 5; 5 & 1; 2 & 4; 4 & 2; 3 & 3)

7 has 6 ways (1 & 6; 6 & 1; 2 & 5; 5 & 2; 3 & 4; 4 & 3)

8 has 5 ways;9 has 4 ways; 10 has 3 ways; 11 has 2 ways; 12 has only 1 way.

That totals 36 possible ways of scoring with two dice.

So score 2 has probability 1/6; 3 has probability 2/6 = 1/3; 4 has probability 3/6 = 1/2; 5 has probability 4/6 = 2/3.

We want to know the probability of scoring less than 5, which has 6 ways out of 36 = 1/6

Now, all the probabilities must total exactly 1, so the probability of scoring at least 5 must be 1 - 1/6 which is 5/6 = 0.83333333333 (the 3 reoccurs ) = 83.33333(recurring)% or just over 83%