Answer:
a) not independent
b) not mutually exclusive
Step-by-step explanation:
Given:
- A 6 sided die is rolled
- Event A is rolling an even number
- Event B is rolling a prime number
Find
- (a) Are A and B independent events?
- (b) Are A and B mutually exclusive events?
Solution:
- We will find the probability of each event:
set(Even number: A) = {2, 4, 6} = 3 outcomes
set(Prime number: B) = {2 , 3, 5} = 3 outcomes
- The probabilities are:
P(A) = 3/6 = 0.5
P(B) = 3/6 = 0.5
- For Event A and B to be independent then the following condition must match:
P ( A & B ) = P(A)*P(B)
set (A&B) = {2} = 1 outcome
P(A&B) = 1/6
1 / 6 = 0.5*0.5
1/6 = 0.25 ...... NOT INDEPENDENT
- For Event A and B to be mutually exclusive then the following condition must match:
P(A&B) = 0
P(A&B) = 1/6
Hence, we can say the events are NOT MUTUALLY EXCLUSIVE
