Suppose that the events A, B and C are mutually independent with P(A)=1 /2, P(B)=1/3 and P(C)=1/4. Compute P(AB U C). Note: the answer is 3/8. Show the steps to get to the final answer.
Suppose that the events A, B and C are mutually independent with P(A)=1 /2, P(B)=1/3 and...
2) Suppose A and B are independent events, then) is incorrect. A P(AB) P(A) ( PCA n B) = P(A)P(B) P(AIB) = P(A) ⓑ P(A u B)-P(A) + P(8)
1. (a) Two events A and B are such that P(A)=1/4,P(A/B)=1/2,and P(B/A)=2/3.Are A and B independent events? Are A and B mutually exclusive events? (b) How many sample of size 4 can be drawn without replacement from the population 0,3,6,3,18?compute the sampling distribution of the mean, then identify the relationship between the population and sampling distribution standard deviations?
In a sample space, events A and B are independent, events B and C are mutually exclusive, and A and C are independent. a) Show that P(AUB) = P(B) + P(A)P(B') = P(A) + P(A')P(B) b) If P(AUBUC) = 0.9, P(B) = 0.5 and P(C) = 0.3 find P(A).
Suppose the events B and B2 are mutually exclusive and complementary events, such that P(B) = 0.12 and P(B2) = (1 – 0.12). Consider another event A such that P(AB) = 0.49 and P(A|B2) = 0.46 Complete parts (a) through (d) below. • Find P(Bin A). • Find P(B2n A) • Find P(A) using the results in parts (a) and (b). • Find P(B1A). (Round the result to 4 decimal places.) a. P(Bin A) b. P(B2N A) c. P(A) DID...
Chapter 3 3.2 Independent and Mutually Exclusive Events 40. E and Fare mutually exclusive events. P(E)-0.4; P(F) 0.5. Find P(E1F) 41.J and Kare independent events. PUlK) 0.3. Find PC) 42. Uand V are mutually exclusive events. P(U) 0.26; P(V)-0.37. Find: a. P(U AND V)= 43.Q and R are independent events. PQ) 0.4 and P(Q AND R) 0.1. Find P 3.3 Two Basic Rules of Probability Use the following information to answer the next ten exercises Forty-eight perc Californians registered voters...
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)?
d) If A and B are mutually exclusive events, then P (An B) = 1// P (A) 2/1 0 3|| (A) + P (B) 4// P (A) + P (B) - P (A and B) e) If A and B are independent events, then P (AJB) 1-P(B) 2-P(A) 3-P(A)P(B) 4-P(A)+P(B)
Suppose that P(X)-0.32, P{Y)-0.44, and P(XUY)-0.58. (a) Are the events mutually exclusive? (b) Are they independent? (c) Calculate PXY. (d) Calculate P(IX).
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.
T-1 Suppose two events A and B are mutually exclusive and PAI 0, P[B] 0 . Consider the following statements: i) P(An B)=0 ii) P(A U B) = P(A) + P(B) iii) A and B are statistically independent. Choose the correct statement. A) Only i) is true. B) Only ii) is true. C) Only iii is true. D) Only i) and i) are true. E) i), ii) and iii) are all true.