Two dice are rolled and someone indicates that the two numbers that come up are different. find the probability that the sum of the two numbers is 4.

Two dice are rolled.

On rolling a die, there are 6 outcomes.

So, total number of outcomes on rolling two dice =

= 36

Since, the two numbers that come up are different.

So, total outcomes will be 36 minus the numbers who comes up same.

Total number of outcomes that come with same numbers

={(1,1) (2,2), (3,3), (4,4), (5,5) and (6,6)} = 6

So, total number of outcomes = 36-6 = 30

The outcomes with the sum of the two numbers is 4 with the condition that the two numbers that come up are different.=

={(1,3) (3,1)}

So, total number of outcomes with the sum of the two numbers is 4 = 2

SO, Probability = Favorable outcomes Total outcomes

Probability  =

=

Therefore, the probability that the sum of the two numbers is 4 is 0.07

1/5^2 = 7.56/45