1. Let (S;F;P) be a probability space with A 2 F and B 2 F such...
1. Let (S;F;P) be a probability space with A 2 F and B 2 F such that P(A) = 0:3 and P(B) = 0:4. Find the following probabilities under the specified conditions. Note that I don’t expect you to have to show much work in answering this question. (a) either A or B occurs if A and B are mutually exclusive (b) either A or B occurs if A and B are statistically independent (c) either A or B occurs if A is a subset of B (d) A occurs but B does not occur if A and B are mutually exclusive (e) A occurs but B does not occur if A and B are statistically independent (f) A occurs but B does not occur if A is a subset of B (g) both A and B occur if A and B are mutually exclusive (h) both A and B occur if A and B are statistically independent (i) both A and B occur if A is a subset of B (j) B occurs but A does not occur if A is a subset of B *Can you please go through the concepts please. Im very confused about the problem.
Homework Answers
Q1) Consider two events P and Q. a. Write the general formula used to calculate the probability that either event P occu...
Q1)
Consider two events P and Q.
a. Write the general formula used to calculate the probability
that either event P occurs or Q occurs or both occur.
b. How does this formula change if:
i. Events P and Q are disjoint (i.e., mutually exclusive of each
other).
ii. Events P and Q are nondisjoint events that are statistically
independent of each other.
iii. Events P and Q are nondisjoint events that are
statistically dependent of each other.
Q2)
Rewrite...
Suppose that A and B are mutually exclusive events for which P(A) = 0.2 and P(B)...
Suppose that A and B are mutually exclusive events for which P(A) = 0.2 and P(B) = 0.7. What is the probability that a. either A or B occurs? b. A occurs but B does not? c. both A and B occur? d. neither A nor B occurs?.
Suppose event A occurs with probability 0.21 and event B occurs with probability 0.72.
Events A and B are mutually exclusive. Suppose event A occurs with probability 0.21 and event B occurs with probability 0.72.a. Compute the probability that A does not occur or B does not occur (or both).b. Compute the probability that either B occurs without A occurring or A and B both occur.
O PROBABILITY Probabilities involving two mutually exclusive events Events A and B are mutually exclusive. Suppose...
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
Suppose event A occurs with probability 0.4 and event B occurs with probability 0.58
Events A and B are mutually exclusive. Suppose event A occurs with probability 0.4 and event B occurs with probability 0.58a. Compute the probability that B occurs or A does not occur (or both).b. Compute the probability that either B occurs without A occurring or A and B both occur.
S) Suppose that A and B are mutually exclusive events for which P(A) = 0.3 and...
S) Suppose that A and B are mutually exclusive events for which P(A) = 0.3 and P(B) = 0.5 What is the probability that (a) either A or B occurs? (b) A occurs and B does not occur? (c) both A and B occur? 4.) A forest contains twenty elk, of which five are captured, tagged and then released. Some time later, four elk are captured from this population. What is the probability that exactly two of these are tagged?...
Events A and B are mutually exclusive. Suppose event A occurs with probability 0.04 and event...
Events A and B are mutually exclusive. Suppose event A occurs with probability 0.04 and event B occurs with probability 0.52. Compute the probability that B occurs or A does not occur (or both).Compute the probability that either A occurs without B occurring or A and B both occur.
Consider the following scenario: • Let P(C) = 0.2 • Let P(D) = 0.3 • Let...
Consider the following scenario: • Let P(C) = 0.2 • Let P(D) = 0.3 • Let P(C | D) = 0.4 A) FIND P(C AND D)= B)Are C and D mutually exclusive? Why or why not? C and D are mutually exclusive because they have different probabilities. C and D are not mutually exclusive because P(C) + P(D) ≠ 1 There is not enough information to determine if C and D are mutually exclusive. C and D are not mutually...
Events 4 and B are mutually exclusive. Suppose event A occurs with probability 0.52 and event...
Events 4 and B are mutually exclusive. Suppose event A occurs with probability 0.52 and event B occurs with probability 0.13, a. Compute the probability that A occurs or B does not occur (or both). b. Compute the probability that either A occurs without B occurring or A and B both occur.
Q3.2 Let (12, F,P) be a probability space. Decide whether each of the following statements hold....
Q3.2 Let (12, F,P) be a probability space. Decide whether each of the following statements hold. (i) 0 is independent of ), and N is independent of 12; (ii) If E is any event which is independent of itself, then either E = 0 or E = N; (iii) If E is any event which is independent of itself, then either P(E) = 0 or P(E) = 1; (iv) If events A and B are both disjoint and independent, then...
Q1)
Consider two events P and Q.
a. Write the general formula used to calculate the probability
that either event P occurs or Q occurs or both occur.
b. How does this formula change if:
i. Events P and Q are disjoint (i.e., mutually exclusive of each
other).
ii. Events P and Q are nondisjoint events that are statistically
independent of each other.
iii. Events P and Q are nondisjoint events that are
statistically dependent of each other.
Q2)
Rewrite...
Suppose that A and B are mutually exclusive events for which P(A) = 0.2 and P(B) = 0.7. What is the probability that a. either A or B occurs? b. A occurs but B does not? c. both A and B occur? d. neither A nor B occurs?.
Events A and B are mutually exclusive. Suppose event A occurs with probability 0.21 and event B occurs with probability 0.72.a. Compute the probability that A does not occur or B does not occur (or both).b. Compute the probability that either B occurs without A occurring or A and B both occur.
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
S) Suppose that A and B are mutually exclusive events for which P(A) = 0.3 and P(B) = 0.5 What is the probability that (a) either A or B occurs? (b) A occurs and B does not occur? (c) both A and B occur? 4.) A forest contains twenty elk, of which five are captured, tagged and then released. Some time later, four elk are captured from this population. What is the probability that exactly two of these are tagged?...
Events 4 and B are mutually exclusive. Suppose event A occurs with probability 0.52 and event B occurs with probability 0.13, a. Compute the probability that A occurs or B does not occur (or both). b. Compute the probability that either A occurs without B occurring or A and B both occur.
Q3.2 Let (12, F,P) be a probability space. Decide whether each of the following statements hold. (i) 0 is independent of ), and N is independent of 12; (ii) If E is any event which is independent of itself, then either E = 0 or E = N; (iii) If E is any event which is independent of itself, then either P(E) = 0 or P(E) = 1; (iv) If events A and B are both disjoint and independent, then...
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