1.

A number is chosen at random from the set {1,2,3,4,....,n} . Let E_(1) be the event that the number drawn is divisible by 2 and E_(2) be the event that the number drawn is divisible by 3, then

Answer»

`E_(1)` and `E_(2)` are ALWAYS independent
`E_(1)` and `E_(2)` are independent if `n=6k(KIN N)`
`E_(1)` and `E_(2)` are independent if `n=6k+2(k in N)`
`E_(1)` and `E_(2)` are dependent if n = 10

Solution :S = {1, 2, 3, , ...n}
`E_(1)=` No. is DIVISIBLEBY 2.
`E_(2) ` = No. is divisible by3.
If n = 6ksay n = 6
S={ 1, 2, 3, 4, 5, 6 }
`P(E_(1))=(3)/(6)=(1)/(2), P(E_(2))=(2)/(6)=(1)/(3)`
`P(E_(1) NN E_(2))=(1)/(6)=P(E_(1)).P(E_(2))rArr` (B) is correct.
If n = 6k say n = 8
S = { 1, 2, 3, 4, 5, 6, 7, 8 }
`P(E_(1))=(4)/(8)=(1)/(2), P(E_(2))=(2)/(8)=(1)/(4)`
Here, `P(E_(1) nnE_(2))=(1)/(8)=P(E_(1))P(E_(2))rArr ` (C) is correct.
Note that : `P(E_(1)nnE_(2))=(1)/(10)!=P(E_(1)).P(E_(2))`
`rArr` Not independent `rArr`dependent.


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