Question

1. a) Give an example of two events that are independent. Prove that your example is correct computationally.


b). Explain why being a dog and being a cat are mutually exclusive.

c) Give an example of two characteristics that are not mutually exclusive and explain why they are not.

Answer 1

a) Two events are said to be independent if the occurrence of one does not affect the occurrence of another. Say,A= Getting a 6 on a roll of a die and B= getting a heads on the Flip of a coin. These two events are independent. Since, P(A) = 1/6 and P(B) = 1/2

And P(A and B) = 1/6*1/2 = 1/12 = P(A)*P(B)

Hence the two events are independent.

b) Two events are mutually exclusive when both cannot occur together. So say if it's a dog, it can't be a cat and if it's a cat it can't be a dog, so they are mutually exclusive.

c) Non mutually exclusive events: In case of rolling a die, the Event of Getting an even number and the Event of Getting a number less than 5 are non mutually exclusive events.

Since both the above events have common elements (2,4) so they can both occur at the same time and hence they're non mutually exclusive events.