Asingle 6-sided die is rolled twice. the set of 36 equally likely outcomes is {(1,1), (1,2), (1,3), (1,4), left parenthesis 1 comma 5 right parenthesis comma(1,5), left parenthesis 1 comma 6 right parenthesis comma(1,6), left parenthesis 2 comma 1 right parenthesis comma(2,1), left parenthesis 2 comma 2 right parenthesis comma(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), left parenthesis 4 comma 4 right parenthesis comma(4,4), left parenthesis 4 comma 5 right parenthesis comma(4,5), left parenthesis 4 comma 6 right parenthesis comma(4,6), left parenthesis 5 comma 1 right parenthesis comma(5,1), left parenthesis 5 comma 2 right parenthesis comma(5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)}. find the probability of getting two numbers whose sum is greater than 9 and less than 13.

The probability of getting two numbers whose sum is greater than 9 and less than 13 is

Step-by-step explanation:

Given : A single 6-sided die is rolled twice.

To find : The probability of getting two numbers whose sum is greater than 9 and less than 13 ?

Solution :

The set of 36 equally likely outcomes,

          1              2              3              4               5             6

1(1, 1)(1, 2)(1, 3)(1, 4)(1, 5)(1, 6)

2(2, 1)(2, 2)(2, 3)(2, 4)(2, 5)(2, 6)

3(3, 1)(3, 2)(3, 3)(3, 4)(3, 5)(3, 6)

4(4, 1)(4, 2)(4, 3)(4, 4)(4, 5)(4, 6)

5(5, 1)(5, 2)(5, 3)(5, 4)(5, 5)(5, 6)

6(6, 1)(6, 2)(6, 3)(6, 4)(6, 5)(6, 6)

Getting two numbers whose sum is greater than 9 and less than 13

The favorable outcome is (4,6),(5,5),(5,6),(6, 4),(6, 5),(6, 6) = 6

The probability is given by,

Therefore, The probability of getting two numbers whose sum is greater than 9 and less than 13 is

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step-by-step explanation: