Probability Distribution
Binomial Distribution
Geometric Distribution
Hypergeometric Distribution
Miscellaneous
100
Which of the following statements is a discrete random variable
a. The time it takes you to complete your test
b. The height of the students in this class
c. Distance between your home and school
d. Number of pairs of shoes you own
d. Number of pairs of shoes you own
100
Which of the following statement is not a characteristic of a binomial distribution
a. All trials must be independent
b. Each trial must be a success or failure
c. All trials must be dependent
d. The number of successes in the trials is counted
C. All trials must be dependent
An outcome of a trial will not affect the outcome of another trial.
100
Which of the following statements is geometric?
a. The number of emails you receive until it is Mr Osachoff
b. The number of times Mr Osachoff emails you to remind you to hand in your project
c. The number of times Mr Osachoff calls your parents
d. The number of times your mom calls you
a. The number of emails you receive until it is Mr Osachoff
100
True or False:
You cannot use hypergeometric distributions whenever the probability of success changes depending on the outcome of previous trials.
False
100
A bag contains 3 red skittles and 5 green skittles. You randomly select 4 skittles. Which distribution can be used to determine the probability that you choose 2 red balls.
a. Binomial
b. Geometric
c. Hypergeometric
c. Hypergeometric
200
Determine which of the following distributions is not a probability distribution. Explain.
D. is not a probability distribution because the values of P(x) ≠ 1
200
Fill in the blanks:
A binomial experiment has ____ possible outcomes: _______________
A binomial experiment has 2 possible outcomes: success or failure.
200
What is the probability that a family doesn't have a baby boy until their 3rd child?
The probability that a family doesn't have a baby boy until their 3rd child is 0.13 or 13%
200
Fill in the blanks:
Hypergeometric distributions are ________ probability distributions. It is used to determine the probability of obtaining a number of successes without ___________.
Hypergeometric distributions are discrete probability distributions. It is used to determine the probability of obtaining a number of successes without replacement.
200
About 93% of people pass their G2 test.
What is the probability it will take someone more than two times to pass their driving test?
The probability it will take someone more than two times to pass their G2 is 0.0049 or 0.5%
300
What probability distribution variable is created from flipping a coin 4 times and recording the number of times you land tails. Explain.
Discrete probability distributions.
Flipping a coin is created from a categorical variable.
300
Explain why the following statement may or may not be a binomial experiment:
Mr Osachoff shuffled a deck of cards. He turned over the top card and did not replace it. He repeated the process 5 times.
P(x) where x = the card you observe.
Is not a binomial experiment.
The trials are not identical and there are more than 2 possible outcomes.
300
Explain whether geometric distributions are continuous or discrete random variables.
Geometric distributions are discrete because you count occurrences.
300
Explain why the following question does not fit a hypergeometric distribution:
What is the probability that 10 out of 40 people are left-handed if 10% of the group is left-handed?
It does not fit a hypergeometric distribution because...
- do not count the number of successes in a sequence of trials
- each trial is independent; hypergeometric distributions are dependent
300
Explain the notation of each variable in the binomial distribution formula: P(x) = nCr px qn-x
nCr → The number of ways to choose a sample of elements from a set of a number of objects
P → probability of successful trials
n → number of independent repetitions
q → probability of failure of each repetition (q=1-p)
x → number of successes that occur
n - x → number of failures that occur
400
The following list is a list of tire pressures measured last week. What is the expected number of inflated tires when Mr Osachoff checked for tire pressures after one week?
x - P(x)
0 - 0.30
1 - 0.25
2 - 0.25
3 - 0.15
4 - 0.05
The expected number of inflated tires is 1.4 tires.
400
What is the probability that more than 7 out of 10 surgeries will be successful when the probability of having a successful surgery is 90%?
The probability that more than 7 out of 10 surgeries will be successful is 0.93 or 93%
400
The probability of a bag of Lays potato chips being underfilled is 68%.
What is the probability that the first bag of potato chips bought from a vending machine that is underfilled is the 6th bag of chips bought?
The probability that the first bag being underfilled is the 6th bag bought is 0.0022 or 22%
P(x) = (1-0.7)5-1 0.7 = 0.00567
400
In a bag of 16 different candies, you draw a candy 4 times.
What is the expected probability that you draw your favourite candy only twice?
The expected probability that you draw your favourite candy only twice is 0.5 or 50%
E(x) = 4(2/16) = 0.5
400
At Richview, a new math class has an 8% passing rate in making students learn the material from grades 9-12 in one year.
If 15 people are known to have not taken any math courses during all of high school, what is the probability that at least 2 students will be able to pass the class?
The probability that at least 2 students will be able to pass the class is 0.34 or 34%
500
An investor estimates that at the end of the year, there is a 40% chance a rare toy will be worth $50, a 35% chance it will be worth $60, and a 25% chance that will be worth $70. What expected value does the investor assign to this stock's end-of-the-year price?
The investor assigns $58.50 to the year-end price.
500
A factory produces pencils in which 1% are defective. The pencils are packed in boxes of 10. A box is then selected at random. What is the probability that there are at least 2 defective pencils in a box?
The probability that there are at least 2 defective pencils in a box is 0.0043 or 4%
500
Mr Osachoff is playing a chess tournament against a computer program and the probability that he wins against the computer is 0.25.
What is the probability that Mr Osachoff has to play more than 4 games before he wins for the first time?
The probability that Mr Osachoff has to play more than 4 games before he wins for the first time is 0.316 or 32%
500
You start at a corner five blocks south and five blocks west of Mr Osachoff. You walk north and east while he walks south and west.
What is the probability that you and Mr Osachoff will meet during your stroll?
The probability that you and Mr Osachoff will meet during your stroll is 0.246 or 25%
500
There is an 80% chance that a Calico cat has 13 black spots. You go to a cat show and count the black spots on Calico cats.
What is the probability that you will review the spots on 3 cats before you find one that has 13 black spots?
The probability that you will find a cat with 13 black spots on your third cat is 0.0064 or 0.6%
P(x) = (1-0.80)3 0.80 = 0.0064