The probability for event a is 0.3, the probability for event b is 0.6, and the probability of events a or b is 0.8.why are the events not mutually exclusive?

The events are not mutually exclusive because the P(A and B)=0.1 not 0

Step-by-step explanation:

Mutual exclusive events are those that can't happen at the same time.For example Tossing a coin, Head and Tail are mutually exclusive events because you can't get a Head and a tail at  the same time.Another example is turning left and turning right are mutually exclusive because you can't do both at the same time.

If events are mutually exclusive, they can happen at the same time.

Mathematically,the probability of mutual exclusive events follows;

P(A and B)=0 The probability of A and B together equals 0

P(A or B) = P(A)+P(B)The probability of A or B equals the probability of A plus the probability of B.

In this question you are given;

P(A)=0.3

P(B)=0.6

P(A or B) =P(A) + P(B)= 0.3+0.6 =0.9

0.9≠0.8 thus the events are not mutually exclusive.