CMAT 2019 Solved Question Paper

Question : 18 of 100

Marks: +1, -0

In a simultaneous throw of a pair of dice, find the probability of getting a total of 9 or more.

$5/18$
$5/12$
$2/7$
$2/36$

Solution:

When a pair of dice are thrown simultaneously the maximum sum possible is 12.The possible cases of getting a sum of 9 are:

\table \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:

\table \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:

\table \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:

\table \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

=10/36=5/18

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