The outcomes that fall in A∩B are {5} only.
What do we mean by the intersection of events?
The intersection of two or more events is the number of outcomes that are common to both events. It is represented by an inverted-U sign, '∩'.
How do we solve the given question?
We are said that Ramona is playing a board game with two number cubes.
∴ All possible outcomes when the cubes are rolled by Ramona are:
(1,1) (1,1) (1,1) (1,1) (1,1) (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)
We are given two outcomes,
A = {the sum of the number cubes is odd}
B = {the sum of the number cubes is divisible by }
When we sum numbers on cubes for each outcome, we get
2 3 4 5 6 7
3 4 5 6 7 8
4 5 6 7 8 9
5 6 7 8 9 10
6 7 8 9 10 11
7 8 9 10 11 12
The outcomes with odd sum are:
(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) (6,5)
∴ A = {3, 5, 7, 9, 11}
The outcomes with sum divisible by 5 are:
(1,4) (2,3) (3,2) (4,1) (4,6) (5,5) (6,4)
∴ B = {5,10}
Now, we check for common terms in A and B to find A∩B.
We only have one common term in A and B, which is 5.
∴ A∩B = {5}
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