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

ok

step-by-step explanation:

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq