Solve the below problems:
Q1. For two events, A and B, P(A) = 0.4, P(B) = 0.2, and P(A/B)=0.6
a. find P(A and B)
b. find P(B/A)
Q2. An experiment results in one of three mutually exclusive events, A,B, or C. It is known that P(A) =.30, P(B) = .55 and P (C) = .15. Find each of the following probabilities:
a. P(A U B)
b. P(A and C)
c. P(A/B)
d. P(B U C)
e. are B and C independent events? Explain
Q3. Two fair coins are tossed, and the following events are defined:
A: {observe at least one head}
B: {observe exactly one head}
a. Draw a Venn diagram for the experiment, showing events A and B. Assign probabilities to the sample points.
b. Find P(A), P(B), and P(A upside down U B)
c. Use the formula for conditional probability to find P(A/B) and P(B/A). Verify your answer by inspecting the
Venn diagram and using the concept of reduced sample spaces.
Q4. Two fair dice are tossed and the following events are defined:
A: {sum of the numbers showing is odd}
B: {sum of the numbers showing is 9, 11, 12}
Are events A and B independent? Why