Exam #1 Test Questions Prob

Home

Get App

Create

Independence

An urn has 3 red balls and 5 blue balls. Suppose 8 balls are selected at random & with replacement. What is the probability the first 3 are red and the last 5 are blue?
- P(R): 3/8
- P(B): 5/8
=
Bayes Formula

In transmitting dot and dash signals a communication system changed 1/4 of dots to dashed & 1/3 of dashes to dots. If 40% of signals transmitted are dots & 60% are dashes, what is the probability that a dot received was actually transmitted as a dot?
- Let T denotes event randomly selected signal is a dot.
- Let R denote event randomly selected signal received is a dot.
- Then denotes a randomly selected transmitted signal is a dash.
- The denotes a randomly selected received signal is a dash.
Find the prob. that a dot received was actually transmitted as a dot. That is, find P(T|R).
- R^c --> Received a dash; T --> Transmitted a dot
- R --> Received a dot; T^c= Transmitted a dot
- P(T)= 40% = 0.4 P(T^c)= 60% = 0.6
- Probability of transmitting a dot Probability of transmitting a dash
Bays Formula:
- P(R|T) =
- = 1- 0.25
- = 0.75
- = 0.6
Total Probability

Suppose 40% of students of a campus are women. If 20% of the women and 16% of the men of this campus are A students, what percent of all of them are A students?
- Let W be event person selected at random is a women.
- Therefore, is event person selected at random is a man.
- Now let event 'A' be a randomly selected student who is an A student.
- P(A|W)= 0.20
- P(W)= 0.40
- P(A) = (0.20)*(0.40) + (0.16)*(0.60)
- = 0.176
- = 17.6%
Conditional Probability

Suppose that 15% of population of a country are unemployed women are total people unemployed is 25%. What percent of unemployed people are women?
- W= Event randomly selected person is a women
- U= Event randomly selected person is unemployed
P(W|U) = % of unemployed women
Multiplication Rule

In a trial, the judge is 65% sure Susan has committed a crime. Robert is a witness who knows if Susan is innocent of guilty. However, Robert is Susan's friend and will lie with 25% if Susan is guilty. He will tell the truth if she is innocent. What is the probability he commits perjury. What if he lies and she is guilty?
- G= event Susan is guilty
- L = event Robert lies
- so, G⋂L= event Susan is guilty & Robert lies
We want to find P(G⋂L)
- P(G)= 0.65
- P(L|G)= 0.25
- so, P(G⋂L)= P(L|G)*P(G)
- = (0.25)*(0.65)
- = 0.1625 = 16.25%
Combinations

From an ordinary deck of 52 cards, seven cards are drawn at random and without replacement. What is the probability that at least one card is a King?
- K= event that at least 1 king is chosen
- event that no king is chosen
so,
Permutations

Suppose that two anthro books, four computer science boojs, three statistics books, and two bio books are put onto a shelf in random arrangement. What is the probability that books of the same subject are together?
- Let A= events that books of the same subject are together
- 1st number of arrangement of 11 books
- = # of permutations of 11 books
- = 11!
- so, N= 11!
Now we count up N(A).

Suppose we have 2 anthro books together, followed by 4 csc books, followed by 3 stats books, and 2 bio books.
- There are:
- 2! to arrange anthro books
- 4! to arrange csc books
- 3! to arrange stats books
- 2! to arrange bio books
so, 2!*4!*3!*2! ways to arrange them. But we could also arrange them 3 stast, 4 csc, 2 bio, 2 anthro, ect. ect. ect.
- Since there are 4 types of books:
- 2!*4!*3!*2! = 4!*2!*2!*3! = ect.
so N(A)= 4!(2!*4!*3!*2!)
- so
- = 0.000128267

Author

GoBroncos

364315

Card Set

Exam #1 Test Questions Prob

Description

Updated

2024-05-02T00:48:55Z

Show Answers