|Compound Probability Problems|
Algebra 2 pg. 744
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.
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?
PT: Compound Probability
RW: Drunk Driving
Assuming the following statistics to be
true, calculate the following probabilities:
Probability of a driver:
a) P (being intoxicated and having an
b) P (being unintoxicated and having an
c) P (being intoxicated, arrested and
d) P (being intoxicated, arrested and
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!!!
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?
Gordon-Holliday Pre-calculus, p. 783
Compound Probability, Complementary Events
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
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.
Probability, Independent Events, Complimentary Events
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
P (of rectangle A) = P (blue ball and yellow club)
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: