Independent events

[csswenso]

A probability experiment is conducted in which the sample space of the experiment is S={1,2,3,4,5,6,7,8,9,10,11,12,13}. let the event A={3,4,6,9,} and event B={2,5,7,13}

a) Are the events A and B mutually exclusive?
Yes because none of the numbers can occur at the same time, they are all different numbers.
b) Are the events A and B independent? Justify your answer numerically.
P(A)=P (A given B) A= 4/13 B=4/13 yes they are independent
c) Are the compliments of events A and B independent? Justify your answer numerically.
A=4/13 B-4/13 the compliment of A = 9/13 and the compliment of B=9/13 and 4/13 does not equal 9/13 they are not independent because they are not equal

Parts b and c are wrong, but I am confused as to why. Could someone please explain.

 

[royhaas]

Independence means that P(A and B) = P(A)P(B).

 

[csswenso]

Do I have the values of P(A) and P(B) correct?

And is what your saying : if I multiply P(A) and P(B) they will be independent if that value equals P(A)?

 

[royhaas]

Independence means that the probability that A and B occur together equals the probability that A occurs, times the probability that B occurs. No more, No less. Your numbers for P(A), P(B) are correct.