An urn contains four balls numbered 6, 10, 14 and 210. A ball is selected at...
An urn contains four balls numbered 6, 10, 14 and 210. A ball is selected at random. Let A be the event the ball is divisible by 3; B the event it is divisible by 5; C the event it is divisible by 7. Show that A and B are independent events, B and C are independent events and A and C are independent events. Are A, B and C independent events?
Homework Answers
P(A) = P(Selected ball is divisible by 3) = 
{6 and 210 are divisible by 3}
P(B) = P(Selected ball is divisible by 5) =
{10 and 210 are divisible by 5}
P(C) = P(Selected ball is divisible by 7) =
{14 and 210 are divisible by 7}
So, 
Now, since 
So, A and B are independent, A and C are independent and B and C are independent.
Also, 
So, A, B and C are not independent events.
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