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NOTE: Please read this after you have mastered the other four sections.


Example 17
What is the probability that rolling two identical dice together will result in a 3 and a 4?

Answer: Think Bottom to Top
Bottom: We have two dice being rolled, with 36 total outcomes possible.
Top: There are two outcomes that can happen: (3,4) and (4,3).
Probability: 2/36 = 1/18

Example 18
What is the probability that rolling two identical dice together will result in the sum of the dice adding to 7?

Answer: Think Bottom to Top
Note: We saw this question above in example 14. Try solving it a different way.
Bottom: Total outcomes = 36
Top: How many of those outcomes yield a 7? Just list them:
(1,6) (2,5) (3,4) (4,3) (5,2) (6,1)

There are 6 in total.

Probability: 6/36 = 1/6

Example 19
Bowl X has 4 cards in it, numbered 1 - 4. Bowl Y has 5 cards in it, numbered 5 - 9. What is the probability that the sum of a card pulled randomly from Bowl X and a card pulled randomly from Bowl Y will equal 8?

Answer: Think Bottom to Top
Bottom: How many different pairs of cards can be pulled? There are 4 cards in Bowl X and 5 cards in Bowl Y. Using permutations: 4 × 5 = 20. So there are 20 total outcomes possible.
Top: Which pairs work for this question?
(1,7) (2,6) (3,5)
3 outcomes.
Probability: 3/20

Example 20
Bowl X has 4 cards in it, numbered 1-4. Bowl Y has 5 cards in it, numbered 5-9. What is the probability that the product of a card pulled randomly from Bowl X and a card pulled randomly from Bowl Y will be even?

Answer: Think Bottom to Top

Chapter 6: Extra Questions