Suppose we have ten balls in a large drum; these balls are numbered 1 through 10
ID: 1179641 • Letter: S
Question
Suppose we have ten balls in a large drum; these balls are numbered 1 through 10. We pick one ball from the drum and define the following events: the ball has an even number on it the ball has a number greater than 7 on it the ball has a number less than 5 on it Are A and B independent? Rigorously justify your answer. Are A and C independent? Rigorously justify your answer. Are B and C independent? Rigorously justify your answer. Note that B and C are exclusive. Comment on this in conjunction with your answer to part (c), and generalize the result.Explanation / Answer
1)No A and B are not independent as number greater than 7 contains 8 and 8 is an even number so they are not independent.
2)Again A nad C are not independent as 4 or 2 are less than 5 and even numbers.
3)Yes they are independent as they have no common region .
4)B = [ 8 ,9 ,10]
c = [4,3,2,1]
as A intersection C = null so they are independent