Question 1

Round answers to two digits after the decimal point.

Given two events E and F with Pr(E) = 0.4, Pr(F) = 0.5, and Pr(EnF) = 0.3,

a) Pr(E|F) =

b) Pr(F|E) =

c) Are E and F independent? (Enter YES or NO)

Question 2

Round answers to two digits after the decimal point.

Given two events E and F with Pr(E) = 0.4, Pr(F) = 0.5, and Pr(EuF) = 0.7,

a) Pr(E|F) =

b) Pr(F|E) =

c) Are E and F independent?

Question 3

In the Happiest City in the World, 50% of the residents are Fine, 80% of the residents are Dandy, and 10% of the residents are neither Fine nor Dandy.

a) What percent of the residents are both Fine and Dandy?

b) Given that a resident is Fine, what is the probability that this resident is also Dandy?

c) Are being Fine and being Dandy independent?

Question 4

Each of four robot archers is to fire one shot at a cell phone. Since they are robots with no emotions, we assume their shots are mutually independent. If the probabilities that these robots hit their targets are 0.4, 0.5, 0.3, and 0.3, what is the probability that at least one of them hits the target? Round answer to 4 digits after the decimal point.

Question 5

In the future, all spokespersons will be robots because it is hard to tell if a robot is lying based on its facial expressions, making them ideal for companies and people who need solid, good, highly efficient lying spokespersons. This particular robot named TikFacTok is programmed in the following manner:

Statement 1: True with probability 0.9.

Statement 2; True with probability 0.4 if first statement is true, otherwise true with probability 0.5.

a) Draw a tree diagram based on given information. This part carries no credit but it will be beneficial for you. You can email the teacher your tree diagram if you are not sure if it is correct.

b) What is the probability that the robot makes one true statement followed by one false statement?

c) What is the probability that the robot makes one true statement and one false statement, in any order?

d) What is the probability that the robot makes two true statements?

e) What is the probability that the robot makes two false statements?

Round answers to the hundredths place.

Question 6

Six people are given six identical envelopes. One of the envelopes contains three tickets to the Disneyland, the other five are empty. They will pick the envelopes based on seniority. The oldest person gets to pick an envelope first, if this envelope contains the tickets, the drawing is over and everyone goes home. If the first envelope is empty, the second oldest person then picks an envelope from the remaining five and checks if this envelope contains the tickets. This process continues until one person picks the envelope that has the tickets. The youngest person feels mistreated and wants to reverse the order. The oldest person gets upset that the youngest is not compliant so they get into a heated argument. Your job is to convince them, using a tree diagram, that there is no difference either way they go.

Question 7

70% of propane tanks used by a company are from factory A, the other 30% are from factory B. Of the tanks from A 4% are defective, and from B 8%. If a randomly selected tank is found to be defective,

a) What is the probability that the tank is from factory A?

b) What is the probability that the tank is from factory b?

Round answer to the hundredths place.

Question 8

25% of students at a college are 35 or older, and of those, 13% are from out-of-state. Of the students that are under 35, 35% are from out-of-state. If a student is randomly chosen and found to be from out-of-state, what is the probability that this student is younger than 35? Round answer to the hundredths place.

Question 9

7 panthers, 7 tigers, and 9 lions gather to plan a global strategy for big cats. 2 of the panthers are pink, 3 of the tigers are pink, and 5 of the lions are pink. If a cat is randomly selected and found to be pink, what is the probability that this cat is a pink panther? Round answer to the hundredths place.