Answer:
a) False
b) True
Step-by-step explanation:
Given : The chance of A is [tex]\frac{1}{3}[/tex]; the chance of B is [tex]\frac{1}{10}[/tex]
To find : True or false, and explain ?
Solution :
a) If A and B are independent, they must also be mutually exclusive.
Two events are mutually exclusive, if the events cannot occur at the same time.
When events A and B are independent, then the chance of event B is not affected by event A occurring.
However, when events A and b are mutually exclusive, then the chance of event B needs to change to 0 when event A has occurred as B cannot occur when A occurs.
Which means the given statement is false.
(b) If A and B are mutually exclusive, they cannot be independent.
Two events are independent, if the probability that one event occurs in no way affect the probability of the other event occurring.
When events A and B are mutually exclusive, then the chance of event B needs to change to 0 when event A has occurred as B cannot occur when A occurs.
Which means, the given statement is true.
