Probability Distribution
Binomial Distribution
Geometric Distribution
Hypergeometric Distribution
Miscellaneous
100
True or False:
The probability distribution of a continuous random variable cannot be described graphically.
False
100
True or False:
An important requirement for a random variable to be binomial is where there are multiple possible outcomes.
False
100
Which of the following statements is incorrect about geometric distributions:
a. Trials are independent
b. There can only be two possible outcomes
c. Defined as a continuous probability distribution
d. Can have an indefinite number of trials
c. Defined as a continuous probability distribution
100
True or False:
You select 5 cards from a deck of cards.
The probability that you select 2 or fewer spades is 0.907 or 90%
True
100
In order for something to be a probability distribution, all probabilities must be equal to which two values?
All probabilities must be equal to 0 or 1
200
What is the missing probability of the following probability distribution?
0 - 0.12
1 - 0.16
2 - 0.24
3 - 0.32
4 - x
5 - 0.05
The missing probability is x = 0.13
200
The probability that a school soccer team will win is 0.6.
What is the probability of losing 3 matches out of 5?
The probability they will lose 3 matches out of 5 is 0.2304
200
Explain how to find the expected value of a geometric distribution.
Divide 1 by the probability of success on each trial.
200
You need to find a store that carries coloured printer ink. You know that only 10% of stores in your area have coloured ink.
You randomly call each store until one has the ink you need.
What are the values of p = success and q = failure?
p = 0.1
q = 0.9
200
A die is tossed 5 times.
What is the probability of getting exactly 2 fours?
The probability of getting exactly 2 fours is 0.161 or 16%
P(x) = 5C2 (0.167)2 (0.833)3
300
Identify which of the two events are discrete or continuous probability distributions.
Explain the difference between the two distributions.
Event A: The number of thunderstorms per year
Event B: Amount of ice in a tea glass
Event A: discrete probability
Event B: continuous probability
Differences: Discrete distribution is countable while continuous is measurable
300
Consider the following statement:
You flip 4 coins two times and count the number of times the coins land tails.
Give 3 reasons why this is a binomial experiment.
1) Consists of repeated trials
2) Only two possible outcomes
3) Trials are independent (one trial will not affect the outcome of the following trials)
4) Probability of success is constant
300
Explain the difference between a geometric distribution and a binomial distribution.
Binomial: has a fixed amount of trials before it begins and X number of successes obtained in that fixed number.
Geometric: has a fixed number of successes and counts the number of trials needed to obtain that first success. Can have an indefinite number of trials.
300
Explain how to tell the difference between a hypergeometric distribution and a binomial distribution.
For a binomial distribution, the probability is the same for every trial.
For a hypergeometric distribution, each trial changes the probability for each following trial because there is no replacement.
300
Identify if the two events are a hypergeometric distribution or geometric distribution, then explain how you can tell the difference between the two concepts.
Event A: Random selection of members for a team from a group of boys and girls
Event B: Asking a group of people if they chose the letter A or B on a test until you find someone who chose the letter in favour.
Event A: Hypergeometric distribution
Event B: Geometric distribution
Differences: For geometric distributions, count the number of failures until the first success. For hypergeometric distributions, count the number of the samples we obtained in a fixed number of trials.
400
Find the expected value of the following probability distribution:
The expected value is E(x)=84.4
400
The probability that you might grab a red M&M out of a bag of M&Ms is 20%.
If there are 24 M&Ms, what is the probability of selecting at least 4 red M&Ms?
The probability of finding at least 4 M&Ms is 0.46 or 46%
400
A baseball player has a batting average of 0.32, which is also the probability that he gets a hit each time he is batting.
What is the probability that he gets his first hit in his third position at bat?
The probability that he gets his first hit in his third position at bat is 0.1480 or 15%
P(x) = (1-0.32)3-1 0.32 = 0.1480
400
You throw darts at a board until you hit the bullseye. Your probability of hitting the bullseye is p=0.17.
You want to find the probability that it takes eight throws until you hit the bullseye.
What is the value of x in P(x)?
The value of P(x)=1, 2, 3, 4, ..., indefinite
400
List 3 reasons why the following statement may or may not be a geometric distribution:
You shake a bag of 30 skittles, with 10 red skittles, 10 blue skittles, and 10 green skittles. You reach for a marble, observe it, then put it back in the bag and shake it again.
You repeat the trials until you reach for a green skittle.
It is a geometric distribution because
1) there are indefinite numbers of trials
2) there are no binary outcomes
3) the trials are independent
500
You pay $1 for a ticket to roll a 6 sided die.
If you roll 1, 2, 3 or 6 you lose. If you roll a 4 you get your money back. If you roll 5, you win $4.
Will you win or lose more money?
What is a fair price for this game?
The expected value is negative, therefore, you will lose more money
A fair price for this game would be $0.83
E(x) = -0.16667 or -$16.6
Fair price = 1 - 0.16667 = 0.8333 or $0.83
500
The probability of a telesales representative making a sale is 0.15.
They need to achieve an expected value of 5 sales per day.
What is the least number of calls each day a representative should make to achieve this requirement?
The representative should make at least 3.33 or 4 calls to reach this requirement.
500
In MDM4U, 27% of students enjoy eating peas.
Let X = the number of students encountered before the first student who enjoys peas is found.
What is the expected number of students who enjoy peas?
The expected number of students who enjoy peas is 2.7037
500
Richview C.I. has 50 teachers, 20 of them are over 40 years old.
Of the 22 English teachers, 12 are over 40 years old.
Compare the expected number of older and younger English teachers in a selected group of 10 teachers.
There are 2.4 older teachers vs 2 younger teachers.
500
10% of applicants for a job at Mcdonald's have the right skills. The manager interviews the applicants one at a time until they find the right candidate.
What is the probability that they will interview at least ten applicants?
The probability that the manager will interview at least ten applicants is 0.0387
P(x) = 9/109 1/10 = 99/1010