Question 1166923: A statistical experiment has ten equally likely outcomes, which are denoted by 1, 2, 3, 4,
5, 6, 7, 8, 9 and 10. Let Event A = {1, 3, 7} and Event B = {6, 8, 10}.
a) Are events A and B mutually exclusive?
b) Are events A and B independent?
c) What is the complement of event A and its probability?
Answer by ikleyn(52775)   (Show Source):
You can put this solution on YOUR website! .
a) Yes, the events A and B are mutually exclusive, since the sets A and B are DISJOINT.
b) The events A and B ARE NOT independent.
Indeed, P(A ∩ B) = 0, since the events A and B are mutually exclusive;
from the other side, P(A)*P(B) =  is not zero.
Since P(A ∩ B) =/= P(A)*P(B), the events A and B are not independent.
c) Complement of event A is event {2,4,5,6,8,9,10}, and the probability of this complement event is  = 1 -  .
Solved. // All questions are answered.
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