Suppose that we have two events, A and B, with P(A) .50, P(B) .50, and PA...
Suppose that we have two events, A and B, with P(A)= 0.50, P(B)=0.60, and P(A ∩ B) = .40 a. Find P(A | B) (to 4 decimals). b. Find P(B | A) (to 4 decimals). c. Are A and B independent? Why or why not?
Suppose that we have two events, A and B, with P(A) = 0.50, P(B) = 0.60, and P(A ∩ B) = 0.05. If needed, round your answer to three decimal digits. (a) Find P(A | B). (b) Find P(B | A). (c) Are A and B independent? Why or why not? A and B _____ independent, because _____ P(A).
Suppose that we have two events, A and B, with P(A) = 0.40, P(B) = 0.70, and P(A ∩ B) = 0.20. (a) Find P(A | B). (b) Find P(B | A). (c) Are A and B independent? Why or why not?
31. Assume that we have two events, A and B. that are mutually exclusive. Assume further that we know P(A) 30 and P(B) a. What is P(A n B)? b. What is P(A I B)? c. 40. A student in statistics argues that the concepts of mutually exclusive events and inde- pendent events are really the same, and that if events are mutually exclusive they must be independent. Do you agree with this statement? Use the probability information in this...
Suppose two events A and B are two independent events with P(A) > P(B) and P(A U B) = 0.626 and PA กั B) 0.144, determine the values of P(A) and P(B).
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...
Suppose that we have two events E and F such that their union is the entire sample space and P(E)=1/3 and P(F)=2/3. Are they independent? Explain.
Assume that we have two events, A and B, that are mutually exclusive. Assume further that we know P(A)= 0.30 and P(B)= 0.40. Assume that we have two events, A and Br that are mutually exclusive. Assume further that we know P(A) 0.30 and PCB 0.40 If an amount is zero, enter "0". a. What is P(An B)? b. what is p(AIB? C. Is AIB) equal to A)? Are events A and B dependent or independent? d. A student in...
Suppose A and B are two events for which P(A) =0.18, P(B) = 0.45, and P(A or B) = 0.54. Find P( A and B) Find Are A and B mutually exclusive? (Support your answers!) Are A and B independent?
The prior probabilities for events A1 and A2 are P(A1) = .50 and P(A2) = .50. It is also known that P(A1 A2) = 0. Suppose P(B | A1) = .10 and P(B | A2) = .04. Are events A1 and A2 mutually exclusive? Compute P(A1 B) (to 4 decimals). Compute P(A2 B) (to 4 decimals). Compute P(B) (to 4 decimals). Apply Bayes' theorem to compute P(A1 | B) (to 4 decimals). Also apply Bayes' theorem to compute P(A2 |...