In a simultaneous throw of a pair of dice, find the probability of getting a total of 9 or more.
When a pair of dice are thrown simultaneously the maximum sum possible is 12.
The possible cases of getting a sum of 9 are:
dice 1 dice 2
four five.....................(1)
five four.....................(2)
six three....................(3)
three six.......................(4)
So a total of 4 cases are possible
The possible cases of getting a sum of 10 are:
dice 1 dice 2
four six......................(1)
six four.....................(2)
five five.....................(3)
So a total of 3 cases are possible
The possible cases of getting a sum of 11 are:
dice 1 dice 2
five six...................(1)
six five..................(2)
So a total of 2 cases are possible
The possible cases of getting a sum of 12 are:
dice 1 dice 2
six six.....................(1)
So a total of 1 case is possible.
Total number ways of getting a sum of 9 or more = 4 + 3 + 2 + 1 = 10 ways
Total outcomes when two dice are rolled simultaneously = 6 * 6 = 36 ways
Probability of getting a sum of 9 or more = Expected number of outcomes/ Total outcomes
= $$\frac{10}{36}$$
= $$\frac{5}{18}$$
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