Question

A red and a green die are rolled. Chart or graph the sample space, and find the odds that the numbers on the dice differ by 1 or more

Answer 1

A red and a green die are rolled then

the sample space is as

(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)

now , event is numbers on the dice differ by 1 or more

A=numbers on the dice differ by 1 or more

A={ (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) }

here out of 36 pairs 30 have an numbers on the dice by 1 or more.

now the odds are defined as the ratio of the probability of the occurrence of an event to the probability of the nonoccurrence of the event

here

here the odds that the numbers on the dice differ by 1 or more is defined as

that is in given case it is defined as

After simplification, we get the

that is

therefore here the odds that the numbers on the dice differ by 1 or more is 5.

Result: the odds that the numbers on the dice differ by 1 or more is 5.