Help with probability

Question

A fair die is rolled and a fair coin is tossed. The random variable X is defined as the number obtained on the die minus the number of heads (0 or 1) resulting on the coin. Calculate and write down a probability table for X.

Answer 1

The sample space for rolling a die together with flipping a coin consists of ordered pairs (1...6 , H or T). There are 12 such pairs and they are equally likely.

 

The possible outcomes for X are

 

0: (1,H)

1: (1,T) or (2,H)

2: (2,T) or (3,H)

3: (3,T) or (4,H)

4: (4,T) or (5,H)

5: (5,T) or (6,H)

6: (6,T)

 

So the probability table is

 

x   |   P(X = x)

-----------------

0   |   1/12

1   |   1/6

2   |   1/6

3   |   1/6

4   |   1/6

5   |   1/6

6   |   1/12