i have some questions about rolling the dice algebra aWhat

i have some questions about rolling the dice ( algebra)

a)What is the probability of getting one even number and one odd number when you roll two dice?

b)What is the probability of getting two distinct numbers if you roll two dice?

c)What is the probability of getting a total between 5 and 8 if you roll two dice?

Note: here between means we include the end points.

thank you.

Solution

a)   one even number and one odd number when rolling 2 dice =(1,2),(1,4),(1,6) , ( 2,1 ) , (2,3) ,(2,5) ,(3,2) ,(3,4) ,(3,6) ,(4,1) ,(4,3),(4,5) , (5,2) ,(5,4) ,(5,6) ,(6,1) ,(6,3) ,(6,6)

total favourable outcomes = 18

total outcomes when rolling 2 dice = 36

therefore , probability of getting one even number and one odd number when you roll two dice = 18/36 = 1/2

b) favourable outcomes of getting 2 distinct numbers = (1,2) (1,3) , (1,4) , (1,5) , (1,6) ,(2,1) , (2,3) , (2,4) , (2,5 ) , (2,6) ,(3,1) , (3,2) , (3,4) ,(3,5) ,(3,6) , (4,1) ,(4,2) ,(4,3) ,(4,5) , (4,6) , (5,1) , (5,2) , (5,3),(5,4) , (5,6) , (6,1),(6,2),(6,3) (6,4) (6,5)

therefore, probability = 30/36 = 5/6

c) total favourable outcomes of getting total between 5 and 8 = 20

probability = 20 / 36 = 5/9