Given P(A) = 0.3 and P(B) = 0.4, do the following. (a) If A and B are mutually exclusive events, compute P(A or B). (b) If P(A and B) = 0.2, compute P(A or B).

Q: Suppose that A and B are independent events such that P(A) = 5/8 and P(B) = 4/7. Find P(A&B).

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Q: Given P(A) = 0.3 and P(B) = 0.4, do the following. (a) If A and B are mutually exclusive events,…

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Q: For events A and B, using the axioms of probability, prove that P(AB) ≤ P(A).

A: For events A and B, using set theory, A=A∩B+Bc∩APA=PA∩B+PBc∩APA=PAB+PBcAPA=PAB+PBcAPAB=PA-PBcA⋯⋯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.

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Q: Suppose P(E) = 0.3, P(F) = 0.5, and P(E or F) = 0.7. Are the events E and F are mutually exclusive?…

A: It is given that P(E) = 0.3 and P(F) = 0.5.P(E) + P(F) = 0.3+0.5 = 0.8.

Q: Suppose A and B are mutually exclusive events, and that P(A)=0.13 and P(B)=0.85. Find P(A OR B)

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Q: Find the following probabilities if A and B are disjoint (mutually exclusive) events, and P(A) =…

A: Given P(A)=0.2 and P(B)=0.3 Both A and B are disjoint (mutually exclusive) events. Disjoint Events:…

Q: For two events E and F, P(E) = 0.30, P(F) = 0.40, and P(E U F) = 0.70. Are E and F mutually…

A: Introduction: The occurrences that cannot occur or cannot occur at the same time are said to be…

Q: If X and Y are mutually exclusive events with P(X) = 0.295, P(Y) = 0.32, then P(X/Y)=?

A: Given X and Y are mutually exclusive events P(X) = 0.295, P(Y) = 0.32 If X and Y are mutually…

Q: Suppose A and B are two independent events with P(a)=0.5 and P(b)=0.4 what is the P(A U B)?

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Q: Assume that A and B are events. If ​P(A∪​B)=0.6​, ​P(A)=0.5​, and ​P(B)=0.25​, find ​P(A∩​B).

A: Given information- We have given that A and B are events.  P(A)=0.5, P(B)=0.25​, P(A∪​B)=0.6​ We…

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: Suppose two events A and B are independent, with P(A) ≠ 0 and P(B) ≠ 0. By working through the…

A: Probability: If a random experiment results in n mutually exclusive and equally likely outcomes; out…

Q: Use probabilities, rather than your own personal experience, to determine whether E and F are…

A: Given information: Given that a die is rolled once. The event E = Getting a 1 and the event F =…

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

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Q: I. Find P(C U B). J. Are C and B mutually exclusive events? Show why or why not.

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Q: you are givin the information that P(A) = 30 and P(B) = 0.40. Do you have enough information to…

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Q: Given that A and B are independent events, show that A and B are also independent events.

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Q: Compute the probability of each of the following events (i) X <1 1/2 (ii) XY is even

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Q: Let A  and B be two events such that P (A) = 0.46 and P (B) = 0.07 (a) Determine P (A ∪ B), given…

A: Given: A and B be two events such that P (A) = 0.46   P (B) = 0.07

Q: Suppose P(E) = 0.3, P(F) = 0.5, and P(E and F) = 0. Are the events E and F are mutually exclusive?…

A: It is given that P(E) = 0.3, P(F) = 0.5 and P(E and F) = 0.

Q: The P ( A ) = 0.16 and the P ( B ) = 0.16 . Events A and B are mutually exclusive. What is the P (…

A: Two events are said to be mutually exclusive, if they cannot both occur at the same time. Here A,B…

Q: For this problem, assume that Pr[A∪B]=0.55Pr[A∪B]=0.55 and Pr[A]=0.25Pr[A]=0.25. (1) What is…

A: P(A or B) =0.55 and P(A) =0.25. Events A and B are independent.

Q: If E and F are independent events with P(E) =0.4 and P(E or F) = 0.6,then find P(F).

A: It is given that E and F are independent events. The given probabilities are PE=0.4  and PE or…

Q: Let A and B be events such that P(A) = 0.6, P(B) = 0.5and P(A∪ B) = 0.8.Find P(A B)). Are A and B…

A: We have given that events  P(A) =0.6 P(B) =0.5 P(A∪ B) = 0.8 Note: According to Bartleby expert…

Q: b) Given that A and B are independent events, show that A and B are also independent events.

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Q: Given  P(A) = 0.6  and  P(B) = 0.4,  do the following. (a) If A and B are independent events,…

A: If A and B are two independent events, then it is known that P(A and B) = P(A)P(B).

Q: Let ? and ? be two mutually exclusive events. Given that (?)=0.25 and ?(?∪?) =0.77, determine ?(?).

A: Given: P(A)=0.25 P(A∪B)=0.77

Q: Decide whether the following pairs of events are dependent or independent. A red and a green die are…

A: The given statement is "A red and a green die are rolled. A is the event that the red die comes up…

Q: Suppose that E and F are two events and that P(E and F)=0.48, P(F)=0.55, and P(E)=0.5. What is P(F…

A: Suppose that E and F are two events and that P(E and F)= 0.48 P(F)=0.55 and P(E)=0.5 What is P(F |E)…

Q: AA and BB are independent events. If Pr(A∩B)=0.28 and Pr[A]=0.4, what is Pr[B]?

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Q: If A and B are mutually exclusive events, then prove that P ( A )<P ( B° )

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Q: If A and B are dependent events such that P(A) = 5/8  and P(B|A) = 3/7, find P(A ∩ B).

A: Given data, P(A) = 5/8   P(B|A) = 3/7 P(A ∩ B)=?

Q: if two events A and B are manually exclusive, what is the value of P(A and B)?

A: If two events not occur at same time,then those events are called as mutually exclusive events.

Q: Let E and F be independent events with P(E) = 0.15 and P(F) = 0.2. What is the probability that at…

A: Given: PE=0.15PF=0.2 E and F are independent events, so: PE∩F=PE×PF=0.15×0.2=0.03

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: Let A, B and C be three independent events such that P(A)=P(B)=0.3 and P(C)=0.5. Find the…

A: It is given that the, P(A) = P(B) = 0.3 and  P(C) =0.5 and since these 3 events are independent.

Q: Which of the following notation is used for not mutually exclusive events? * P(A or B) = P(A) + P(B)…

A: Given that  Two events A and B are mutually exclusive events.  P(A or B)=P(A)+P(B)

Q: Suppose that C and D are mutually exclusive events such that P(C) = 0.14 and P(D) = 0.32. Determine…

A: Given, P(C) = 0.14  P(D) = 0.32  P(C or D)=?

Q: J A and B are independent events, prove that the events A and B,A and B; and A and B are also…

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Q: For this problem, assume that Pr[A∪B]=0.85 and Pr[A]=0.5Pr[A]=0.5. What is Pr[B] if A and B are…

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Q: For this problem, assume that Pr[A∪B]=0.85and Pr[A]=0.3. (1) What is Pr[B]Pr[B] if A and B are…

A: (1) Given that A and B are independent events.  that means Pr[A∩B]=Pr[A]×Pr[B]   So from the union…

Q: AA and BB are independent events. If Pr[A]=0.3Pr[A]=0.3 and Pr[B]=0.5Pr[B]=0.5, what is…

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Q: Can you explain: P(M^c ) union P(R)= P(M^c) +P(R) I thought this was true for only mutually…

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Q: Suppose A and B are mutually exclusive events, and that P(B)=0.44 and P(A OR B)=0.81. Find P(A).

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Q: Consider the following two events for a randomly selected adult: Y = N = this adult has shopped on…

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Q: Which pair(s) of events are Mutually Exclusive.

A: In a competition, two people will be selected from four finalists to receive first prize and second…

Q: 4. Determine whether each of the following pairs of events is independent:

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