Question

Suppose that a fair, 6 sided die is rolled. Let X indicate the event that an odd number is rolled (in other words, X = 1 if an odd number is rolled and X = 0 otherwise). Let Y indicate the event that 2, 3, or 4 is rolled (in other words, Y = 1 if 2, 3, or 4 is rolled and Y = 0 otherwise). Find P (X = 0, Y = 1).

Answer 1

`(1)/(3)`

Explanation:

We are given that a fair 6 sided die is rolled.

Let X denotes the event that an odd number

X=1, if an odd number

X=0, if an even number

Let Y indicates the event that 2,3 or 4 is rolled .

Y=0,if 1,5 or 6 rolled

Y=1 , if 2,3 or 4 rolled

We have to find P(X=0,Y=1)

It means we have to find P(2 or 4).

When X=0 and Y=1 It means we get an even number.

P(2 or 4)=P(2)+P(4)=
`(1)/(6)+(1)/(6)=(2)/(6)=(1)/(3)`

Hence, P(X=0,Y=1)=
`(1)/(3)`