QUESTION
1.
Question 1
Prompt 1: For each of the following scenarios, find the requested probability. Assume the sets AA, BB, and CC are events from the same sample space SS. (Hint: Venn diagrams may help with the visualization, although they are not required to answer the questions.) If P(A) = .4P(A)=.4, P(B^c) = .7P(Bc)=.7, and P(A ∩ B^c) = .2P(A∩Bc)=.2, find P(A ∩ B)P(A∩B)
1 point
2.
Question 2
Prompt 1: For each of the following scenarios, find the requested probability. Assume the sets AA, BB, and CC are events from the same sample space SS. (Hint: Venn diagrams may help with the visualization, although they are not required to answer the questions.)
If P(A) = 0.9P(A)=0.9 and P(B) = 0.9P(B)=0.9, what is the lower bound for P(A \cup B)P(A∪B).
1 point
3.
Question 3
Prompt 2: Three popular options on a certain type of car are AA leather seats, BB a sunroof, and CC heated seats. In the past, P(A) = 0.55P(A)=0.55 (i.e. 55% of the customers have requested option A), P(B) = 0.45P(B)=0.45, P(C) = 0.4P(C)=0.4. Furthermore, P(A ∩ B) = 0.25P(A∩B)=0.25, P(A ∩ C) = 0.2P(A∩C)=0.2, P(B ∩ C) = 0.15P(B∩C)=0.15 and P(A ∩ B ∩ C) = 0.1P(A∩B∩C)=0.1. Find the probability that a customer will ask for at least one of the three options.
1 point
4.
Question 4
Prompt 2: Three popular options on a certain type of car are AA leather seats, BB a sunroof, and CC heated seats. In the past, P(A) = 0.55P(A)=0.55 (i.e. 55% of the customers have requested option A), P(B) = 0.45P(B)=0.45, P(C) = 0.4P(C)=0.4. Furthermore, P(A ∩ B) = 0.25P(A∩B)=0.25, P(A ∩ C) = 0.2P(A∩C)=0.2, P(B ∩ C) = 0.15P(B∩C)=0.15 and P(A ∩ B ∩ C) = 0.1P(A∩B∩C)=0.1.
Find the probability that a customer will not ask for any of these three options.
1 point
5.
Question 5
Prompt 2: Three popular options on a certain type of car are AA leather seats, BB a sunroof, and CC heated seats. In the past, P(A) = 0.55P(A)=0.55 (i.e. 55% of the customers have requested option A), P(B) = 0.45P(B)=0.45, P(C) = 0.4P(C)=0.4. Furthermore, P(A ∩ B) = 0.25P(A∩B)=0.25, P(A ∩ C) = 0.2P(A∩C)=0.2, P(B ∩ C) = 0.15P(B∩C)=0.15 and P(A ∩ B ∩ C) = 0.1P(A∩B∩C)=0.1.
Find the probability that a customer will ask for heated leather seats but not a sunroof.
1 point
6.
Question 6
Prompt 2: Three popular options on a certain type of car are AA leather seats, BB a sunroof, and CC heated seats. In the past, P(A) = 0.55P(A)=0.55 (i.e. 55% of the customers have requested option A), P(B) = 0.45P(B)=0.45, P(C) = 0.4P(C)=0.4. Furthermore, P(A ∩ B) = 0.25P(A∩B)=0.25, P(A ∩ C) = 0.2P(A∩C)=0.2, P(B ∩ C) = 0.15P(B∩C)=0.15 and P(A ∩ B ∩ C) = 0.1P(A∩B∩C)=0.1.
Find the probability that a customer will ask for at most two of the options.
1 point
7.
Question 7
Prompt 2: Three popular options on a certain type of car are AA leather seats, BB a sunroof, and CC heated seats. In the past, P(A) = 0.55P(A)=0.55 (i.e. 55% of the customers have requested option A), P(B) = 0.45P(B)=0.45, P(C) = 0.4P(C)=0.4. Furthermore, P(A ∩ B) = 0.25P(A∩B)=0.25, P(A ∩ C) = 0.2P(A∩C)=0.2, P(B ∩ C) = 0.15P(B∩C)=0.15 and P(A ∩ B ∩ C) = 0.1P(A∩B∩C)=0.1.
Find the probability that a customer will ask for exactly two of the options.
1 point
8.
Question 8
Prompt 3: A message of length 5 digits is to be sent. Each digit can be a 0, 1, or 2.
What is the cardinality of the sample space?
1 point
9.
Question 9
Prompt 3: A message of length 5 digits is to be sent. Each digit can be a 0, 1, or 2.
If every message is equally likely, what is the probability that the message consists of 2 zeros, 2 ones, and 1 two? Round your answer to have four decimal places.
1 point
10.
Question 10
Prompt 3: A message of length 5 digits is to be sent. Each digit can be a 0, 1, or 2.
What is the probability that the message contains at least one zero? Round your answer to have three decimal places.