Suppose that a fair, 6 sided die is rolled. Let X indicate the event that an even number is rolled (in other words, X = 1 if an even 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: 1/2, 1/2

Step-by-step explanation:

A die has 6 faces.

Total number of faces = 6

Possible outcomes are : 1,2,3,4,5,6

Even numbers : 2, 4, and 6 = 3

Non even numbers: 1,3, and 5 = 3

First statement:

P (Even number) = 3 / 6 = 1/2

P (X=1) = 1/2

P (odd number) = 3/6 = 1/2

P (X=0) = 1/2

Second statement:

P (2) = 1/6

P (3) = 1/6

P (4) = 1/6

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

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

Thus,

P (Y=1) = 1/2

Therefore,

P (X = 0, Y=1) = 1/2, 1/2