Question

Two number cubes are rolled for two separate events: Event A is the event that the sum of numbers on both cubes is less than 10. Event B is the event that the sum of numbers on both cubes is a multiple of 3. List the members of the sample space for event A.

Answer 1

A = {1,2,3,4,5,6,7,8,9}

Explanation:

If we roll two dices we get the possible outcomes:

(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)

outcomes = 36

Numbers that give the sum less than 10 are: (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);(5,1) ; (5,2) ; (5,3) ;(5,4) ;(6,1) ; (6,2) ; (6,3)

Total number of favourable events of numbers on both cubes that give a sum less than 10 = 30

Probability = 30/36

the members of the sample space for event A are:

A = {1,2,3,4,5,6,7,8,9} ....