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Gordon-Holliday Pre-calculus, p. 783

M: Availability

PT: Compound Probability, Complimentary Events

RW: Baseball

The Orioles pitching staff has 5 left-handers and 8 right-handers.  If 2 pitchers are selected at random to warm up, what is the probability that at least one of them is right-hander?

Brown Pre-calculus, p. 612

M: Availability

PT: Compound Probability, Independent Events, Complimentary Events

RW: Playoff Series/Basketball

The championship series of the National Basketball Association consists of a series of at most 7 games between two teams X and Y.  The first team to win 4 games is the champion and the series is over.  At any time before or after a game, the status of the series can be recorded as a point (x, y).  The point A (3,1), for example, means that team X has won 3 games and team Y has won 1 game.  From point A, the series can end in a championship for team X in 3 ways (X, YX, YYX).  If you assume that the team X has a probability of 0.6 of winning each and every remaining game, then the probability that the team X becomes champion from point A is:

P (X) + P (YX) + P (YYX) = 0.6 + (0.4)(0.6) + (0.4)(0.4)(0.6) = 0.936

a)   Find the probability that team Y becomes champion from point A.

b)   If team X has won 1 game and team Y has won 3 games, find the probability that team Y becomes champion.

c)    If team X has won 2 games and team Y has won 1 game, find the probability that team X becomes champion.

Glencoe Algebra 2

PT: Compound Probability, Independent Events, Complimentary Events

RW: Golf

During gym class, Joe needs to pick out a golf ball to play golf.  There are 4 balls left in the bucket: 3 are blue and 1 red.  He also has to pick a club.  Each club has a different color handle: 1 black and 2 yellow-handled clubs are available.  You can create an area diagram that represents Joe’s choice of a golf ball and golf club as follows:  

P (of rectangle A) = P (blue ball and yellow club)

= P (blue ball) * P (yellow club)

=3/4 * 2/3

= 6/12

= 1/2

Questions:

1) The area of the large rectangle made above represents the combined probability of each of Joe’s possible choices.  Find the probability of the other three rectangles B, C, and D.  Explain in your own words what each of these areas represent.

2) What is the length and width of the whole square?  What is its area?  Why do the areas necessarily have to have this value?

3) Now, Joe wants to buy his girlfriend couple of flowers for their big date tonight.  Joe does not have much money, so he can only select two flowers at the shop.  Joe knows that Martisha, his girlfriend, loves daisies and roses.  Once in the shop, Joe approaches the two vases which contain these two types of flowers.  Noticing that one vase contains 1 pink rose, 2 purple roses, 3 red roses, and the other vase contains 1 yellow daisy and 3 white daisies, he decides he cannot decide!  So, Joe closes his eyes and selects one flower from each vase randomly.  Make an area diagram that represents the probabilities of all of Joe’s possible selections.  Describe what each rectangle represents.

Key to Problem Bank: