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Glencoe Algebra 2 pg. 744

PT: Compound Probability, Conditional Probability, Odds

RW: Finding a lost friend

On a recent Today show, two women were profiled who had known each other since childhood in England.  After one of the women married, she moved away and the two women lost contact for 50 years.  One day, while standing in line at a restaurant in California, the women struck up a conversation and each of them realized that she was speaking to her long-lost friend!  After listening to their story, Katie Couric, the host of Today, pointed out that the chances of this happening must be ‘one in a million.’  One of the women, however, said that she believed the chances were probably closer to ‘one in a billion.’  Describe the steps you would take to compute the odds of this occurring.  Be sure to list all of the factors that would have to be considered.

Glencoe Algebra 2

PT: Compound Probability, Independent events

RW: Spelling Bee

You are entering a spelling bee at your school.  You have been practicing at home and have found that you can correctly spell words 94% of the time.

1) What is the probability that you spell the first 5 words correctly?

2) What is the probability that you correctly spell the first 4 and then miss-spell the 5th word?

3) What is the probability that you win the contest by spelling all 25 words correctly?

Glencoe Algebra 2

PT: Compound Probability

RW: Drunk Driving

Assuming the following statistics to be true, calculate the following probabilities:

Probability of a driver:

Being intoxicated 0.02

An intoxicated driver:

- Having an unimpeded trip 0.99911

- Having an accident 0.00045

- Being arrested 0.00044

- Having his case dismissed 0.30

- Being convicted of a crime 0.70

Not being intoxicated 0.98

An unintoxicated driver:

- Having an unimpeded trip 0.99984

- Having an accident 0.00016

a) P (being intoxicated and having an unimpeded trip)

b) P (being unintoxicated and having an unimpeded trip)

c) P (being intoxicated, arrested and convicted)

d) P (being intoxicated, arrested and dismissed)

NOTE:  The probability of an accident involving drinking and driving being fatal and/or destroying many lives is 99.99%!  DO NOT DRINK AND DRIVE!!!

Merrill Algebra 1

PT: Compound Probability

RW: Leaf Landing

A leaf is blown onto a hopscotch court and lands on one of the six squares of the T-shaped figure below.  It is then randomly blown to an adjacent square.  What is the probability that the leaf end up on a red square?

 Green Yellow White Red Blue Orange

Gordon-Holliday Pre-calculus, p. 783

M: Availability

PT: Compound Probability, Complementary 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, Complementary Events

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:

 Blue Ball: 3/4 Red Ball: 1/4 Yellow Club:  2/3 A B Black Club: 1/3 C D

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:

 M: Misconception PT: Probability Topic RW: Real World Topic