Question

Find the probability of getting the sum of two numbers, less than 3 or more than 11 when a pair of distinct dice is thrown together.

Answer 1

When two dice are thrown, the possible outcomes or Sample Space = {(1,1), (1,2), (1,3), ..., (1,6), (2,1),(2,2),...,(2,6), (3,1),(3,2),...,(3,6), (4,1),....(4,6),(5,1)...,(5,6),(6,1),...(6,6)}

So there are total 36 outcomes whech two dice are thrown.

According to question, we have to find the sum of numbers such that they are less than 3 and more than 11.

So, Let E denote the number of outcomes for the required circumstance.

∴ E = {(1,1),(6,6)}

Thus, number of outcomes, n(E) = 2

∴ Required Probability = n(E)/S

= 2/36

= 1/18

Hence, 1/18 is the required probability.