For mutually exclusive events R1​, R2​, and R3​, we have ​P(R1​)=0.05​, ​ P(R2​)=0.4​, and ​P(R3​)=0.55. ​Also, PQ | R1=0.5​, PQ | R2=0.3​, and PQ | R3=0.2. Find P(R3 | Q)

Q: Suppose that A and B are mutually exclusive events. a. Use the special addition rule to express P(A…

A: a. Events A and B are mutually exclusive. Special addition rule is used. Special Addition Rule If…

Q: given that P(E) = 0.8, what must be true about the event E? a) event E is impossible b) event E is…

A: Given that P(E)=0.8  0.8 is very close to 1.

Q: Find P(A and B) if P(A) is 0.3 and the P(B) is 0.4, and events A and B are independent.

A:

Q: Consider two events B and C, such that P(B) = 0.28, P(C) = 0.46, and %3D P(C n B) = 0.2, then P(C n…

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Q: If A and B are events such that ​P(A)equals=0.60 and P(A∪​B)equals=0.70​, find​ P(B) when ​(a) A…

A: (a)If events A and B are mutually exclusive events, then, P (A or B) = P(A)+ P(B).Or, P(B) = P (A or…

Q: For not mutually exclusive events A and B, P(A) = 0.59, P(B)=0.46 and P(A B)=0.28. Find the P(AUB).

A: Given:        The A and B are not mutually exclusive P(A) = 0.59 P(B) = 0.46 P(A ∩ B) = 0.28

Q: Suppose that A and B are events such that: P(A) = —‚P(B) = 10 and P(A or B) = Use rule of sum and…

A: Given Information: p(A)=310p(B)=12p(A or B)=25

Q: Suppose that A, B are two events such that P(A) > 0 and P(B) > 0.  If A and B are not disjoint, then…

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Q: Prove or disprove that for any two events A, and A2, P[A, n A-] 21- PÍAG] – P[A£]

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Q: Suppose that E and F are two events and that P(E and F)=0.1 and P(E)=0.5. What is P(F|E)​?

A:

Q: Given that A and B are mutually exclusive event, find P(A or B) for the following. P(A) =0.41 and…

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Q: For mutually exclusive events R1, R2, and R3, we have P(R,) = 0.05, P(R,) = 0.5, and P(R3) = 0.45.…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: If A and B are independent events such that P(A) = 0.4 and P %3D

A: Concept: If the probability of occurrence of one event is not affected by the probability of…

Q: For mutually exclusive events R,, R2, and R3, we have P(R,)= 0.05, P(R2) = 0.4, and P(R3) = 0.55.…

A: P(R1) = 0.05P(R2) = 0.4P(R3) = 0.55P(Q|R1)=0.5P(Q|R2)=0.6P(Q|R3)=0.6

Q: Suppose that C and D are events such that P(C) = 4/5 and P(C&D) = 3/10. Find P(D| C).

A: The formula for conditional probability is,

Q: If it is impossible for events A and B to occur simultaneously, the events are said to be________ .…

A: Two events are called mutually exclusive if they cannot occur at the same time.   Therefore, If it…

Q: - For any two events A and B; P ( ACO B) =P (B)-P (AOB)

A:

Q: The probability that a person owns a car is 0.85, that a person owns a laptop is 0.45, and that a…

A: Given information- P (own a car) = 0.85 P (own a laptop) = 0.45 P (owns both a car and a laptop) =…

Q: The rule P (E U F) = P (E) + P (F) - P (EN F) is used for: * all events disjoint events O Any two…

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Q: For mutually exclusive events R,, R2, and Ry., we have P(R,) = 0.05, P(R2) = 0.6, and P(R,)= 0.35.…

A: Given that ​P(R1​)=0.05​,​ P(R2​)=0.6​, and​P(R3​)=0.35. ​Also,P (Q | R1)=0.6​,P(Q | R2 )=0.7​,…

Q: For mutually exclusive events R1​, R2​, and R3​, we have ​P(R1​)=0.05​, ​ P(R2​)=0.4​, and…

A: Two events A and B are given. If two events A and B are said to be mutually exclusive events, then…

Q: For mutually exclusive events R,, R2. and R3, we have P(R,) = 0.05, P(R2) = 0.3, and P(R,) = 0.65.…

A: Using law of total probability P(q) = P(q|r1)P(r1) + P(q|r2)P(r2) + P(q|r3)P(r3) We know value for…

Q: (c) State an event which is (i) complementary with G; (ii) mutually exclusive with M.

A: Event: In probability theory, an event is an outcome or a set of outcomes of a random experiment to…

Q: Let A and B be events where P(A) = 1/3 and P(B) = 1/4. Show bounds for P(A intersection B)

A: P(A) = 1/3, P(B) = 1/4.

Q: Suppose that C and D are independent events such that P(C) = 0.7 and P(D) = 0.6. Find (C&D).

A: Two events C and D are said to be independent if,

Q: Consider two events B and C, such that P(B) = 0.28, P(C) = 0.46, and P(C n B) = 0.2, then P(C n B)…

A: Given that P(B) = 0.28, P(C) = 0.46, P(C' AND B) = 0.2

Q: If A and B are events such that ​P(A)=0.2 and ​P(A∪​B)=0.4​, find​ P(B) when ​(a) A and B are…

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Q: Suppose the events B1, B2, ally exclusive and complementary events such that P(B1) = .2, P(B2) =…

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Q: Suppose that C and D are independent events such that P(C) = 3/4 and P(D) = 2/5. Find P(C&D).

A: Given that,C and D are independent eventsP (C) =3/4P (D) =2/5P (C&D) =?

Q: Suppose P(A) = .70, P(B) = .18, and events A and B are mutally exclusive. Find:  a) P(A and B) b)…

A: The provided information are :P(A) = 0.70, P(B) = 0.18The events A and B are mutually exclusive.

Q: 2]. Let the events A = {x 0.75}. (a) Find the probabilities of A, B, A N B, and A Nc. (b) Find the…

A: Calculate the events of A,B and C. A=[-1,0) Since, A=x<0. Given that, B=|x-0.5|<0.5 Thus,…

Q: For mutually exclusive events R,, R2, and R3, we have P(R,) = 0.05, P(R2) = 0.4, and P(R3) = 0.55.…

A: Solution: Let R1, R2and R3 be three mutually exclusive events.  P(R1)= 0.05P(R2)= 0.4P(R3)=…

Q: 5. Consider three events: E1, E2, and F. Assume that P(F) > 0, and that P(E, N E2|F) =…

A: Introduction:  Conditional Probability: Let there are two events , event A and event B. Then the…

Q: The events A and B are mutually exclusive. If ​P(A)=0.6 and ​P(B)=0.2​, what is​ P(A or​ B)?

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Q: For a given event, A, P(A) = 0.34.  For a second given event, B, P(B) = 0.44.  Additionally, P (A ⋃…

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Q: GIVEN P(E) =0.35 P(F) =0.08 AND P( E AND F) =0.402…

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Q: I toss a fair die twice, and obtain two numbers X and Y. Let A be the event that X=2, B be the event…

A: A fair dice have 6 faces 1, 2, 3, 4, 5 and 6 and let X and Y be the two numbers obtained in a toss.

Q: For mutually exclusive events R,, R2, and R3, we have P(R,) = 0.05, P(R2) = 0.5, and P(R3) = 0.45.…

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Q: For mutually exclusive events A and B, P(A)=0.32 and P(B)=0.35 Find P(A | B)

A: Given, P(A) = 0.32 P(B) = 0.35

Q: Suppose A and B are mutually exclusive events such that P(A) = .3 and P(B) = .4. Suppose C is an…

A:

Q: Suppose that the events A, B and C are mutually independent with  P(A) = 1/2 , P(B) = 1/3, P(C) =…

A: Given A,B, and C are mutually independent P(A) = 1/2 P(B) = 1/3 P(C) =  1/4

Q: If P (Event A)=0.2 and P(Event B)=0.3, and the two events are disjoint, then P (Event A and Event B)…

A: Disjoint events : if two events A and B are disjointevents then the two events can not occure at the…

Q: For two events A and B, suppose P(A)=0.6, P(B)=0.2, and P(A|B)=0.7, then P(A U B)= __________.…

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Q: Let A and B be two events such that P(AC) = 0.70, P(B) = 0.50, and P(A U B) = 0.60. What is P(An B)?

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Q: Suppose that in a given town, 60% of the population is under age 40 (event A). It is found that the…

A: Supports inoculation Doesn’t support inoculation Total Under 40 0.72 * 0.60 = 0.432…

Q: Thank you

A: Solution:Independent events are those when the happening of one event does not impact the happening…

Q: For any event A, P (A U Ã) =1 True or false

A: for any event A, A¯  is complement of A. then A¯∩A=∅

Q: Consider two events A and B such that P(A|B) = 0.3, P(A) = 0.6 and P(B) = 0.4. (a) Based on the…

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Q: suppose two events A and B are independent, with P(A) = 0 and P(B) = 0. by working through the steps…

A: 1)   Condition for Independence:   If A and B are independent events, then P(A and B)=P(A)*P(B).…