Question

A die is thrown twice. What is the probability that the same number will come up either time.

Answer 1

A  die has 6 faces marked as 1,2, 3, 4, 5, 6. When we throw a die , than total number of  outcomes = 6 { 1 , 2 , 3 , 4 , 5 , 6 }
But when we throw  two dice simultaneously , than total number of outcomes =  6 × 6 = 36
Total possible outcomes on throwing two dice are:
{(1,1),(1,2),(1,3),(1,4),(1,5),(1,6), (2,1),(2,2),(2,3),(2,4),(2,5),(2,6), (3,1),(3,2),(3,3),(3,4),(3,5),(3,6), (4,1),(4,2),(4,3),(4,4),(4,5),(4,6), (5,1),(5,2),(5,3),(5,4),(5,5),(5,6), (6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}
Number of all possible outcomes=36
SOLUTION:

Total number of outcomes= 36

Favourable outcomes are : (1,1),(2,2),(3,3), (4,4) ,(5,5),(6,6)
Number of outcomes favourable = 6
Probability = Number of favourable outcomes / Total number of outcomes.

Required probability = P(same number will come up either time) = 6 /36

Hence, the probability of getting a same number will come up either time is 1/6.

HOPE THIS WILL HELP YOU...