Question

Toss a fair dice twice. Define the following events:

A ={the sum of the 2 numbers that turn up is odd}
B ={the sum of the 2 numbers that turn up is divisible by 2}
C ={the sum of the 2 numbers that turn up is divisible by 3}

a) Are events A and B ( i) independent; (ii) mutually exclusive; (iii) exhaustive ?

My Ans:
a i) Dependent
a ii) Mutually exclusive
a iii) Exhaustive

b) Are events A and C ( i) independent; (ii) mutually exclusive; (iii) exhaustive ?

b i) Dependent
b ii ) Not Mutually Exclusive
b iii) Not exhaustive.

Answer 1

For the first one, a number cannot be both odd and divisible by two, so they are (ii), mutually exclusive. A and B are also exhaustive, since a whole number will *either* be odd or divisible by two.
For the second one, both A and C can occur together *or* apart, but there are more possible results, so they are (ii), not mutually exclusive.

Answer 2

I think I solved it too, just hope my answers are all right.

Answer 3

@snowpolar Thank for the medal :)