Consider two events A and B whose probabilities are known. It is known that the two events are not mutually exclusive and not independent. Which of the following calculations could be used to compute P(A ∩ Bc)?
P(A ∩ Bc) = P(A) + P(Bc) |
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P(A ∩ Bc) = P(A) • P(Bc) |
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P(A ∩ Bc) = 1- P(A ∩ B) |
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P(A ∩ Bc) = P(A) - P(A ∩ B) |
Consider two events A and B whose probabilities are known. It is known that the two...
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...
O PROBABILITY Probabilities involving two mutually exclusive events Events A and B are mutually exclusive. Suppose event A occurs with probability 0.03 and event B occurs with probability 0.02. a. Compute the probability that A does not occur or B does not occur (or both). b. Compute the probability that neither the event A nor the event B occurs. (If necessary, consult a list of formulas.) 6 2
Two events with nonzero probabilities can be both mutually exclusive and independent cannot be both mutually exclusive and independent are always mutually exclusive cannot be both mutually exclusive and independent and are always mutually exclusive
0 en the events A and B above, find the following probabilities P[ not (A or B)) P(A or B)- P(A and not B) P(A or B but not both) Are events A and B independent (why P(B and not A)- P( not A) or why not) Are events A and B mutually exclusive (why or why not) GRB 4/4/2019 Math 121 HW 6- Probability Rules
2.) In the Venn diagram shown is given the probabilities for An Bº, An B, and An BC Construct a completed contingency table for these events and determine the following: А B a.) Table: 33% 17% @ 15% b.) P(AUB) = c.) P(AB) = d.) Are the events A and B mutually exclusive? Explain your answer. e.) Are the events A and B independent? Explain your answer.
6) (10 points) The prior probabilities for events A1 and A2 are P(A1) = 0.40 and P(A2) = 0.60. It is also known that P(A1 or A2) = 1. Suppose P(BA1) = 20 and P(B|A2) =0.05. a. Are A1 and A2 mutually exclusive? Explain. (2 point) b. What is the probability that A1 does not occur? (2 point) C. Compute P(A2 and B) if A1 and B are independent (3 points) d. Compute P(A1 and B) (3 points)
The events A, B, and C occur with respective probabilities 0.60, 0.10, and 0.28. The events B and Care mutually exclusive; likewise the events B and A are mutually exclusive. The probability of the event СПА is 0.20. Compute the probability of the event (end UB (If necessary, consult a list of formulas.)
The events A, B, and C occur with respective probabilities 0.80, 0.26, and 0.13. The events C and B are mutually exclusive; likewise the events C and A are mutually exclusive. The probability of the event BnA is 0.22. Compute the probability of the event Bn(AUc) (If necessary, consult a list of formulas.)
The events A, B, and C occur with respective probabilities 0.59, 0.53, and 0.36. The events and B are mutually exclusive; likewise the events C and I are mutually exclusive. The probability of the event Bn A is 0.49. Compute the probability of the event BA (AUC). (If necessary, consult a list of formulas.) E х 5
The events A, B, and C occur with respective probabilities 0.24, 0.08, and 0.71. The events A and Care mutually exclusive; likewise the events A and B are mutually exclusive. The probability of the event Cn Bis 0.07. Compute the probability of the event CUBUA (If necessary, consult a list of formulas.) D X $ Com Submit Assignment