Question

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.

Answer 1

Two dice are rolled.

On rolling a die, there are 6 outcomes.

So, total number of outcomes on rolling two dice = $6^2$

= 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 $\div$ Total outcomes

Probability  = $\frac{2}{30}$

= $\frac{1}{15}$

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