Given P(A) = 0.1 P(B) = 0.1
We know that

For two events A and B, to be mutually exclusive,
For two events A and B, to be independent,
Here
but
A and B are mutually exclusive but not independent
(1 point) If P(A) = 0.1, P(B) = 0.1, and P(AUB) = 0.2, then P(An B)...
9. If P(A) = 0.2, P(B) = 0.2, and P(A U B) = 0.4, then P(An B) = (a) Are events A and B independent? (enter YES or NO) (b) Are A and B mutually exclusive? (enter YES or NO)
Suppose that P(A)0.5, P(B)0.2, P(C) 0.3, P(AnB) 0.1 and P(AnC) 0.1. Compute the following: (a) (2 points) P(AUB) b) (6 points) P(A UC) (c) (4 points) Are the events A and B independent? What about A and C? (d) (8 points) If the sets B and C are mutually exclusive sets, what is P(A U B U C)?
5. Suppose A, B are events such that P(A) = 1/3, P(B) = 1/4, find P(AUB) under each of the following assumptions: (a) If A and B are mutually exclusive (disjoint). (b) If A and B independent.
Problem 3: If P(A) 0.2, P(B) 0.1, and P(A or B) PIA U B) 0.28, then (a) (2.5 points) find the P(A and B). That is, find P(AnB). (b) (2 points) clearly explain whether the events A, B are mutually exclusive (disjoint). (c) (2 points) clearly explain whether the events A, B are independent based on probability
1 point) lf P(A)-0.4, P(B)-0.4, and P(A U B) 0.74, then (a) Are events A and B independent? (enter YES or NO) NO (b) Are A and B mutually exclusive? (enter YES or NO) NO
Suppose we have two events A and B. Suppose further that P(A) - 0.1, PB)-0.2, and P(AUB) = 0.3. a. [2 marks] Calculate P(A NB) b. [2 marks] Use the mathematical definition of independence to determine if A and B are independent. Conclude in a single sentence. Use only one of the two appropriate c. [2 marks] Use the mathematical definition of mutual exclusivity to determine if A and Bare mutually exclusive. Conclude in a single sentence. MacBook Air #58...
Two events A and B are such that P(A) = 0.4, P(B) = 0.5, and P(AUB) = 0.7. (a) Find P(A n B). 0.2 (b) Find P(AUB). 0.8 (c) Find P(An B). 0.3 (d) Find P(AB). (Enter your probability as a fraction.) 1/2
Question 5 1 pts If A and B are mutually exclusive events, then P(AB) = P(AUB) Not enough information to answer the question O False O True
Let P(A) = 0.4 P(B) = 0.5 P(A|B) = 0.2 (Please show working). If the events a and b are independent, calculate the P(A and B) If the events a and b are not independent, calculate the P(A and B) If the events a and b are mutually exclusive, calculate the P(A or B)
Given P(A) = 0.6 and P(B) = 0.3 If A and B are mutually exclusive events, compute P(A or B). If P(A and B) = 0.2, compute P(A or B). If A and B are independent events, compute P(A and B). If P(B|A) = .1, compute P(A and B).