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Glencoe Algebra 2

PT: Independent Events, Replacement

RW: Jelly Bean

You are given a bag of 10 jellybeans.  Answer the questions below and explain your conclusions.

1) Draw a jellybean from the bag and record the color.  Put the jellybean back in the bag and repeat this process 10 times.   If you never record that you drew a green jellybean, can you conclude that your bag of jellybeans has no green jellybeans?

2) Suppose that you did this 50 times and you still did not record a green jellybean, can you then conclude that there are no green jellybeans in your bag?

3) How many times do you need to repeat this process of drawing and replacing jellybeans to be absolutely certain that there are no green jellybeans in your bag?

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?

Larson Geometry

PT: Sample Space & Size, Independent Events

RW: Die

Consider rolling polyhedron dice.  Each die are numbered on each face, beginning with one.

What is the probability of:

a)      Rolling a 3 on an octagon die?

b)      Rolling a 3 on an iscosahedron die?

c)      Rolling a 3 on a tetrahedron die?

d)      Rolling a 2-digit number on a dodecahedron die?

e)      Rolling a pair of 8’s on a dodecahedron and octagon dice?

Gordon-Holliday Pre-calculus, p. 794

PT: Bernoulli trials, Binomial Setting, Independent Events

RW: Cooking

In cooking class, 1 out of 5 souffles that Sabrina makes will collapse.  She is preparing 6 souffles to serve at a party for her parents.  What is the probability that exactly 4 of them do not collapse?  What is the probability that exactly 4 collapse?

Gordon-Holliday Pre-calculus, p. 794

PT: Bernoulli trials, Binomial Setting, Independent Events

RW: Skeet Shooting

Skeet shooting involves shooting at discs, called clay pigeons, propelled into the air by a machine.  Heather usually hits 9 out of 10 clay pigeons.  If she shoots 12 times, find the following probabilities:

a)      P(all misses)

b)      P(exactly 7 hits)

c)      P(all hits)

d)      P(at least 10 hits)

Gordon-Holliday Pre-calculus, p. 794

PT: Bernoulli trials, Binomial Setting, Independent Events

RW: Stocks

A stockbroker is researching 13 independent stocks.  An investment in each stock will either make money or lose money.  The probability that each stock will make money is 5/8.  What is the probability that exactly 10 of the stocks make money?  Explain your reasoning.

Gerver Algebra 2, 123-124

PT: Binomial Distribution, Bernoulli trials, Independent Events

RW: Quality Control 

On an assembly line of Acme Radio, the probability that a radio is defective is 1/15.  If an inspector randomly checks 10 items, what is the probability of finding:

a)      exactly 2 defective

b)      no more than 2 defective

c)      at least 3 defective

Brown Pre-calculus, p. 612

M: Availability

PT: Compound Probability, Independent Events, Complementary 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: