Session 8, Part B:
Mathematical Probability

In This Part: Predicting Outcomes | Fair or Unfair? | Outcomes | Finding the Winner
Making a Probability Table

Another way to solve this problem is to look at a probability table for the sum of the two dice. This representation can be quite useful, since it gives us a complete description of the probabilities for the different values of the sum of two dice, independent of the rules of the game. Note 6

Again, here are the sums of the possible outcomes for the two dice:

Red Die

Blue Die

 + 1 2 3 4 5 6 1 2 3 4 5 6 7 2 3 4 5 6 7 8 3 4 5 6 7 8 9 4 5 6 7 8 9 10 5 6 7 8 9 10 11 6 7 8 9 10 11 12

 • Only one of the outcomes (highlighted in purple) produces a sum of 2. There are 36 equally likely outcomes. So the probability of the sum being 2 is 1/36. • Two of the outcomes (highlighted in green) produce a sum of 3. There are 36 equally likely outcomes. So the probability of the sum being 3 is 2/36.

Here is the start of a probability table for the sum of two dice:

Sum

Frequency

Probability

 2 1 1/36 3 2 2/36

Problem B7

Complete the probability table.

Sum

Frequency

Probability

 2 1 1/36 3 2 2/36 4 5 6 7 8 9 10 11 12

Sum

Frequency

Probability

 2 1 1/36 3 2 2/36 4 3 3/36 5 4 4/36 6 5 5/36 7 6 6/36 8 5 5/36 9 4 4/36 10 3 3/36 11 2 2/36 12 1 1/36

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 Problem B8 Use the probability table you completed in Problem B8 to determine the probability that Player A will win the game. Recall that Player A wins if the sum is 2, 3, 4, 10, 11, or 12.

 Problem B9 If you know the probability that Player A wins, how could you use it to determine the probability that Player B wins without adding the remaining values in the table?

 If Player A does not win, then Player B wins.   Close Tip : If Player A does not win, then Player B wins.

 Session 8: Index | Notes | Solutions | Video

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