Define the Word
What is Probability?
The chance that something will happen
What is the formula for Classical Probability?
Number of outcomes in event / Total number of outcomes in the sample space
What does it mean by P(A and B)?
Also known as P(A n B)
P(A) x P(B)
What is the formula for Conditional Probability?
P(B|A)= P(A and B)/ P(A)
A bag has 6 balls labelled A,B,C,D,E,and F
One ball will be randomly picked, and its letter will be recorded as the outcome. Give the sample space describing all possible outcomes. Then give all of the outcomes for the event of choosing the letter A or C.
Sample Space: {A,B,C,D,E, and F}
Event of choosing the letter A or C: {A,C}
Define Outcome
The result of a single trial of a probability experiment
Rolling a die twice what is the outcome of
Event A: the sum is greater than 6
Event B: The sum is an odd number
Round your answer two decimal places
Event A: 21/36 = 7/12 = 0.58
Event B: 18/36 = 0.50
Let A and C be two events such that P(A) = 0.03 and P(C)= 0.94
Do not round your answers
(a) Determine P(A U C), given that A and C are independent
(b) Determine P(A U C), given that A and C are mutually exclusive
Part A = 0.9418
Part B= 0.97
It is estimated that, during the past year, 26% of all adults visted a therapist, 44% of all adults used non-prescription antidepressants, 20% of all adults visted a therapist and used a non-prescription antidepressant during the past year.
Round your answer to 2 decimal places
(a) An adult who visited a therapist during the past year is randomly selected. What is the probability this adult used non-prescription antidepressants?
(b) What is the probability that an adult visited a therapist during the past year, given that he or she used non-prescription antidepressants?
P(used antidepressants | visted therapist) = 0.77
P(visted therapist|used antidepressants)= 0.45
Event X: letter selected is found in the word BAG
Event Y: letter selected comes after C
Give the outcomes for each of the following events.
(a) Event X or Y
(b) Event X and Y
(c) Complement of Event X
(a) Event X or Y: {A,B,D,E,F,G}
(b) Event X and Y:{G}
(c) Complement of Event X:{C,D,E,F}
Define Event
Consists of a set of outcomes of a probability experiment
Rolling a die twice find the probability you will land on a sum greater than 10
Round your answer two decimal places
0.08
Suppose that A and B are independent events such that P(A) = 0.40 and P(Complement B) = 0.70
Find P(A n B) and P(A U B)
P(A n B) = 0.12
P(A u B) = 0.58
Suppose that a certain college class contains 55 students. Of these, 34 are Sophomores, 33 are history majors, and 10 are neither. A students is selected at random from the class.
(a) What is the probability that the student is both a sophmore and a history major?
(b) Given that the student selected is a history major, what is the probability that he is also a sophmore?
Write your response as a fraction or decimal
(a): 2/5 or 0.4
(b): 2/3 or 0.67/0.7
You are given a bag with 8 marbles.
Event A: Marbles are odd numbered
Event B: Marbles are greater than 3
Find the outcomes of the following events
(a) Event A or B
(b) Event A and B
(c) Complement of Event A
(a) Event A or B: {1,3,4,5,6,7,8}
(b) Event A and B:{5,7}
(c) Complement of Event A:{2,4,6,8}
What is Sample Space?
The set of all possible outcomes of a probability experiment
Find the Probability you will roll a die twice and land on a number divisible by 2
Round your answer 2 decimal places
0.50
Let A and C be two events such that P(A) = 0.34 and P(B)= 0.28
Do not round your answers
(a) Determine P(A U B), given that A and C are independent
(b) Determine P(A U B), given that A and C are mutually exclusive
Independent = 0.5248
Mutually Exclusive = 0.62
A fair die is rolled 6 times. What is the probability that a 4 is obtained on at least one of the rolls? Round your answer to three decimal places
0.665
A dartboard has 8 equally sized slices numbered 1 to 8.
The slices numbered 5,6, and 7 are grey
The slices numbered 1,2,3,4, and 8 are white
The dart is tossed and lands on a slice at random
Let X be the event that the dart lands on a grey slice, and let P(X) be the probability of X
Let not X be the event that the dart lands on a slice that is not grey, and let P(not X) be the probability of not X.
P(X): 3/8
P(not X):5/8
What does it mean when something is mutually exclusive or a disjoint event?
Events that can not occur at the same time (they have no outcomes in common)
Find the Probability you will roll a die twice and land on a number divisible by 8
Round your answer 2 decimal places
5/36 = 0.14
Events A and B are mutually exclusive. Suppose events A occurs with a probability of 0.01 and event B occurs with a probability of 0.64
(a) Compute the probability that A occurs or B does not occur (or both)
(b) Compute the probability that either B occurs without A occurring or A and B both occur
(a) 0.36
(b) 0.64
A bag contains 6 blue and 9 yellow marbles. For each conditions below, find the probability of a randomly selecting a blue marble on the first draw and a yellow marble on the second draw.
First Draw: 24%
Second Draw: 26%
A spinner with 12 equally sixed slices is shown below. 3 slices are yellow, 4 are blue, and 5 are red. The dial is spun and stops on a slice at random. What is the probability that the dial stops on a red slice?
Write your answer as a fraction or decimal
5/12 or 0.417/ 0.42