Extra Review Problems

4

A local restaurant offers a Prix Fixe menu, with a choice of an appertizer, an entree and a desert for one price.
If there are 3 choices for the appetizer, 5 choices for the entree and 4 choices for dessert, how many different meals can be ordered?

4

A casino claims that its Roulette Wheel is truly random.
What should that claim mean about the roulette wheel and its sections & colors?

Explain below:

4

A doctor tells a patient just diagnosed with a serious disease that there's a 60% chance she'll live at least 5 years.
Where do you think that probability comes from?
(interpret this probability, remember our answers to the class kick from last week Thurs/Fri)

4

After an unusually dry autumn, a rado announcer is hear to say:
'Watch out! We'll pay for these sunny days later on this winter.'

Explain what he's trying to say and comment on the validity of his reasoning.
Ex. what law is he using? Is his thinking flawed? Why?

4

Commercial airplanes have excellent safety records, nevertheless there are crashes occasionally, with the loss of many lives. In the weeks following a crash, airlines often report a drop in the number of passengers, probabily becausepeople are afraid to risk flying.
A travel agent suggests that since the law of averages makes it highly unlikely to have two crashes within a few weeks of each other, flying soon after a crash is the safest time to fly.

Do you agree? Why or why not?
Think about the laws we have discussed in class.

Use the following information for the first section of problems:
The Masterfoods Company says yellow candies make up 20% of their plain M&M’s, red another 20%, and orange, blue, and green each make up 10%. 
The rest are brown. 
We will assume the M&M's come from an extremely LARGE vat of M&M's.

4

If you pick an M&M at random, what is the probability that it is brown?
P(brown)=

4

If you pick an M&M at random, what is the probability that it is yellow or orange?
P(yellow or orange)=

4

If you pick an M&M at random, what is the probability that it is not green?
P(not green)= 1 - P(green)

4

If you pick an M&M at random, what is the probability that it is striped?
P(striped)=

4

You shake a coin out of a piggy bank containing a quarter, a penny, a dime and a nickel; record the value.

1. select the sample space
2. do you think the events in the sample space are equally likely?

4

You toss 2 fair coins; record the order of heads and tails for the flips.

1. select the sample space
2. do you think the events in the sample space are equally likely?

4

You roll a fair 6 sided die; record if the number is odd or even.

1. select the sample space
2. do you think the events in the sample space are equally likely?

4

A company is testing their batteries in digital cameras to see if they last long enough to take 500 pictures. Each day they test 20 batteries and graph the overall percentage of the batteries that have failed the test so far.

Estimate the probability that one of the company’s batteries will fail before taking 500 pictures with a digital camera. __________ Explain your reasoning.
Ignore the letter 'A' on the graph.

4

A company is testing a newly developed coin to be used in the Super Bowl to determine which team gets to choose how they will start the game.

Estimate the probability that a flip of the coin will give heads. __________
Explain your reasoning.

4

What Statistical law is being illustrated in the previous question?

10

At a high school, some students take Spanish, and some do not. Also, some students take an arts subject, and some do not. Let S be the set of students who take Spanish and A be the set of students who take an arts subject. On the Venn diagrams given, shade the region representing the following instances:

0

A gym runs 2 fitness classes, spin and circuits.
On Saturday, 100 people visited the gym.
18 people attended spin class.
10 people attended both classes.
58 people did not attend either class.

Draw a representation of this in a Venn Diagram:

1

What is the probability that a randomly selected person attended only circut class?

1

What is the probability that a randomly selected person attended exactly 1 class?

0

A random sample of 100 US schools gives us the following information:
14 are overcrowded,
52 have the majority of students on a free lunch program,
and 13 are both.
Draw a Venn Diagram of the situation:

1

What is the probability that a randomly selected school is not overcrowded?

1

Given that the selected school is overcrowded, what is the probability that the majority of students are on the free lunch program?

1

A local restaurant offers a Prix Fixe menu, with a choice of an appertizer, an entree and a desert for one price.If there are 3 choices for the appetizer, 5 choices for the entree and 4 choices for dessert, how many different meals can be ordered?

A casino claims that its Roulette Wheel is truly random. What should that claim mean about the roulette wheel and its sections & colors?Explain below:

A doctor tells a patient just diagnosed with a serious disease that there's a 60% chance she'll live at least 5 years. Where do you think that probability comes from? (interpret this probability, remember our answers to the class kick from last week Thurs/Fri)

After an unusually dry autumn, a rado announcer is hear to say:'Watch out! We'll pay for these sunny days later on this winter.' Explain what he's trying to say and comment on the validity of his reasoning.Ex. what law is he using? Is his thinking flawed? Why?

If you pick an M&M at random, what is the probability that it is brown?P(brown)=

If you pick an M&M at random, what is the probability that it is yellow or orange?P(yellow or orange)=

If you pick an M&M at random, what is the probability that it is not green?P(not green)= 1 - P(green)

If you pick an M&M at random, what is the probability that it is striped?P(striped)=

You shake a coin out of a piggy bank containing a quarter, a penny, a dime and a nickel; record the value.1. select the sample space2. do you think the events in the sample space are equally likely?

You toss 2 fair coins; record the order of heads and tails for the flips.1. select the sample space2. do you think the events in the sample space are equally likely?

You roll a fair 6 sided die; record if the number is odd or even. 1. select the sample space2. do you think the events in the sample space are equally likely?

A company is testing a newly developed coin to be used in the Super Bowl to determine which team gets to choose how they will start the game. Estimate the probability that a flip of the coin will give heads. __________ Explain your reasoning.

What Statistical law is being illustrated in the previous question?

A gym runs 2 fitness classes, spin and circuits.On Saturday, 100 people visited the gym.18 people attended spin class.10 people attended both classes.58 people did not attend either class.Draw a representation of this in a Venn Diagram:

What is the probability that a randomly selected person attended only circut class?

What is the probability that a randomly selected person attended exactly 1 class?

A random sample of 100 US schools gives us the following information:14 are overcrowded,52 have the majority of students on a free lunch program,and 13 are both.Draw a Venn Diagram of the situation:

What is the probability that a randomly selected school is not overcrowded?

Given that the selected school is overcrowded, what is the probability that the majority of students are on the free lunch program?

A local restaurant offers a Prix Fixe menu, with a choice of an appertizer, an entree and a desert for one price.
If there are 3 choices for the appetizer, 5 choices for the entree and 4 choices for dessert, how many different meals can be ordered?

A casino claims that its Roulette Wheel is truly random.
What should that claim mean about the roulette wheel and its sections & colors?

Explain below:

A doctor tells a patient just diagnosed with a serious disease that there's a 60% chance she'll live at least 5 years.
Where do you think that probability comes from?
(interpret this probability, remember our answers to the class kick from last week Thurs/Fri)

After an unusually dry autumn, a rado announcer is hear to say:
'Watch out! We'll pay for these sunny days later on this winter.'

Explain what he's trying to say and comment on the validity of his reasoning.
Ex. what law is he using? Is his thinking flawed? Why?

If you pick an M&M at random, what is the probability that it is brown?
P(brown)=

If you pick an M&M at random, what is the probability that it is yellow or orange?
P(yellow or orange)=

If you pick an M&M at random, what is the probability that it is not green?
P(not green)= 1 - P(green)

If you pick an M&M at random, what is the probability that it is striped?
P(striped)=

You shake a coin out of a piggy bank containing a quarter, a penny, a dime and a nickel; record the value.

1. select the sample space
2. do you think the events in the sample space are equally likely?

You toss 2 fair coins; record the order of heads and tails for the flips.

1. select the sample space
2. do you think the events in the sample space are equally likely?

You roll a fair 6 sided die; record if the number is odd or even.

1. select the sample space
2. do you think the events in the sample space are equally likely?

A company is testing a newly developed coin to be used in the Super Bowl to determine which team gets to choose how they will start the game.

Estimate the probability that a flip of the coin will give heads. __________
Explain your reasoning.

A gym runs 2 fitness classes, spin and circuits.
On Saturday, 100 people visited the gym.
18 people attended spin class.
10 people attended both classes.
58 people did not attend either class.

Draw a representation of this in a Venn Diagram:

A random sample of 100 US schools gives us the following information:
14 are overcrowded,
52 have the majority of students on a free lunch program,
and 13 are both.
Draw a Venn Diagram of the situation: