MATH SOLVE

6 months ago

Q:
# A pair of dice are tossed. what is the probability that doubles are rolled, given that the sum on the two dice is less than 8?

Accepted Solution

A:

(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)

the sum is less than 8, we will remove s which have sum of 8 or more

we have 21

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

(3,1) (3,2) (3,3) (3,4)

(4,1) (4,2) (4,3)

(5,1) (5,2)

(6,1)

the doubles (1.1) (2.2) (3.3)

So 3 out of the 21 are doubles

3/21 = 1/7

the sum is less than 8, we will remove s which have sum of 8 or more

we have 21

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

(3,1) (3,2) (3,3) (3,4)

(4,1) (4,2) (4,3)

(5,1) (5,2)

(6,1)

the doubles (1.1) (2.2) (3.3)

So 3 out of the 21 are doubles

3/21 = 1/7