Question

If events X and Y are independent events then P(XNY) =

Answer 1

If events X and Y are independent events then

P(X N Y) = P(X) . P(Y)

Example:- Consider the experiment of rolling a fair die

sample space = S ={1,2,3,4,5,6}

n=6

X : Occureance of an even number

X = {2,4,6} , m=3

P(X) = m/n = 3/6 = 1/2

Y : Occureance of a number greater than 4

Y = { 5,6}, k= 2

P(Y) = k/n = 2/6 = 1/3

P(X N Y) = P{6} = 1/6 ------1

P(X) . P(Y) = 1/2 * 1/3 = 1/6 --------2

from equation 1 and 2, we get

P(X N Y) = P(X) . P(Y)

Therefore X and Y are independent events