Calculating Probabilities Related to Unions and Intersections
Union and Intersection
Sometimes we need to combine two or more events into one compound event. This compound event can be formed in two ways.
Describing and Finding the Probabilities of Unions and Intersections
Suppose you have a standard deck of 52 cards. Let:
More Describing and Finding
Consider the throw of a die experiment. Assume we define the following events:
Finding Simple Events
Again, we get the empty set.
For the following examples, suppose you have a standard deck of 52 cards. Let:
For 1-3, you are given a “fair die” that has six sides with 1 to 6 dots on them. When the die is tossed or rolled, each of the sides is equally likely to come up. Determine the probability of the following outcomes for the number of dots showing on top after a single roll of the die.
- 5 dots
- two or three dots
- all odd dots
Fro 4-8, suppose you draw one card at random from an ordinary card deck. There are 52 possible cards that you can select.
- Suppose that all possible card selections are equally likely, what probability should be assigned to each selection?
- Find the probability that you choose a face card (J, Q K or A).
- Find the probability that you choose a black card (spade or club).
- Consider the events ``draw a face card" and ``draw a 5 or smaller". Are these events overlapping or disjoint? Explain.
- Find the probability of ``draw a red card" or ``draw a spade".
For 9-12, one of the most popular casino games is roulette. In this game, there is a wheel with 38 numbered metal pockets (1 to 36 plus 0 and 00). The wheel is spun moving a metal ball and the ball comes to rest on one of the 38 pockets. The wheel is balanced so that the ball is equally likely to fall on any one of the 38 possible numbers. You play this game by betting on various outcomes-you win if the particular outcome is spun. What is the probability of winning if you bet on the following?
- Number 32
- Even numbers (2, 4, etc.)
- First 12 numbers (1 to 12)
- Four consecutive numbers, such as 20, 21, 23, 24.
To view the Review answers, open this PDF file and look for section 3.2.