Question

For the two six-sided dice case:

1. Write out the six-by-six matrix showing all possible (36) combinations of outcomes.

2. Draw a histogram of the probability of outcomes for the dice totals.

1. Explain the shape of the histogram.

3. Draw a Venn diagram for the 36 dice roll combinations. Define a set "A" as all the combinations that total seven; define set "B" as all the combinations that have one die roll (either die 1 or 2) equal to 2. Indicate the sets A and B, the intersection of A and B and the union of A and B on the diagram.

4. Mathematically show (using the definition of intersection) the probability of throwing a 3 on die one and a 4 on die two. Use the Venn diagram for guidance.

5. Based on throwing both dice twice, mathematically show (using the definition of union) the probability of throwing:

1. a seven on the first roll or double ones on the second
2. a seven on the first or second roll
3. a seven on the first or any doubles on the second roll

f. Two dice are rolled and the sum of the numbers is even. What is the probability that the sum is greater than 8. Use the definition of conditional probability to answer.

Answer 1