Let A and B be events of a sample space. a. Suppose that A and (not B) are mutually exclusive. Explain why B occurs whenever A occurs.b. Suppose that B occurs whenever A occurs. Explain why A and (not B) are mutually exclusive

Q: Suppose A and B are events in a sample space with P(A) = 0.62, P(B) = 0.67, P(BU A) = 0.91 Find the…

A: Given A and B events of a sample space where; P(A)=0.62P(B)=0.67P(B∪A)=0.91 (a) We know by addition…

Q: Let the sample space be S = {z, m, o, p}. How many events are there?

A: Number of events in sample space = 2n where n is no of outcomes. Here S = {z, m, o, p}  here n=4…

Q: 3. If A, B and D are three events in a sample space where An B = 0 and AU B = S, show that P(D) =…

A: Given that, 3. If A, B and D are three events in a sample space where A∩B = 0 and AUB= S We need to…

Q: 2.4 Let A and B be two events of the same sample space. If P(A|B) P(A) then the events A and B are…

A: Solution- Given that A and B are two events  P(A|B)=P(A)then the event A and B are always…

Q: Construct a Venn diagram to illustrate the possible intersections and unions for the following…

A: Here we use basic form for Venn Diagram.

Q: is a collection of sample points. A(n) O a. probability O b. experiment C. event O d. permutation

A: Experiment is a collection of a sample points.

Q: (6) If A and B are two events of a sample space N such that ACB then P(B|A) = (a) 를 (b)를 (e) 를 (c)…

A: The formula to find P(B|A) is:

Q: If an event A includes the entire sample space, then P(A) = 0. O A. True O B. False

A:

Q: If three events A, B, and C are independent in a sample space S, find weather the following…

A: Given: Three events A, B and C are independent events in a sample space S. The objective is to…

Q: Suppose P(A) = 0.40, P(B) = 0.60, and A and B are mutually exclusive and they complete the sample…

A: Solution:  Given information: P(A)= 0.40 P(B)= 0.60 A and B are mutually exclusive events.

Q: Which of the following is the appropriate definition for the intersection of two events A and B…

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Q: Let A and B be events in a sample space. Suppose that P(A) = 0.3, P(B) = 0.75, and P(A ∩ B) = 0.15.…

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Q: a) Let C and D are some events in sample space S and |S|=15. Given C, set of even number = {2, 4, 6,…

A: Given problem Given that   Let C and D are some events in sample space S and | S | = 15. Given C,…

Q: If A and B are independent events in a sample space S, then P(AIB) equals: OP (A) P (A) * P (B) P…

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Q: Let S be a sample space. Suppose A and B are two independent events on S. Show that the events A°…

A:

Q: Consider the sample space S = {copper, sodium, nitrogen, potassium, uranium, oxygen, zinc} and the…

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Q: Let A, B, and C be three events of the sample space S such that n(S)=60, n(A)=30, n(B)=18, n(C)=36…

A: Given The data is as follows: n(S)=60 n(A)=30 n(B)=18 n(C)=36

Q: Let the sample space be S={1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Suppose the outcomes are equally likely.…

A: Given S={1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. n(S)=10 E={4, 8}. n(E)=2 P(E)=?

Q: Suppose we have two events A and B in the sample space S. If P (B) = P (S).– P(A), then B = A %3D O…

A: Please find the solution

Q: If A and B are two independent events in a sample space S, find weather the following statement is…

A: GivenA and B are independent then (Ac , Bc) and (A,Bc)  also independent

Q: a sample space includes the events A,B& C, draw a venn diagram in which the three events are…

A: Given that, A sample space includes the events A, B and C. We are asked to draw a Venn diagram in…

Q: 1. Suppose that A and B are two mutually exclusive events in a sample space such that P(A) = 1 –…

A: Note- As per our policy we can answer only 1st question. If you want solutions for other, then you…

Q: ne event under the given sample space S = {30, 31, 32, 33 SA = {32, 34, 36, 38}, B = {30, 33, 36,…

A: The sample space is given as S=30,31,32,33,34,35,36,37,38,39 The event A is given by  A=32,34,36,38…

Q: 里 P(A|B) = > _P(A|BnC;)P(C;|B). 7=1

A: It is given that C1, C2, C3...Cn comes from a partition of the sample space. From the given formula…

Q: (4) If two events A and B are in sample space S, then P(S | A) = P(S | B) = 1, P(A| S) = P(A) and…

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Q: Suppose A and B are events in a sample space with P(A)=0.7, P(B)=0.48, P(B∪A)=0.88 answer the…

A: GIVEN DATA :  Two  events A & B in a sample space with PA=0.7, PB=0.48 and PB∪A=0.88       TO…

Q: If E, E, are two events of a sample space S such that E, CE₂, then PE) PE

A:

Q: Consider the Sample Space S={automobile, bus, train, bicycle, boat, motorcycle, airplane}…

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Q: In a sample space, events A and B are such that P(A) = P(B) and P(A and B) = P(A' and B') = p. %3D…

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Q: 1.3 Let A and B be two events of the same sample space. If A and B are independent and P(A) = 0.5…

A: Given,P(A)=0.5P(A∩B)=0.1and A , B are independent events

Q: Let B an event in a sample space S, then P (BIS)equals: * P (S) *P (B) P (1/B) P (B) P (S)/P (B)…

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Q: Let A and B are two event of a sample space S and let P(A) = 0.5, P(B) = 0.7 and P(AUB) = 0.9. Find…

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Q: Let S be a sample space and E and F are independent events associated with S. Suppose that Pr(E)=…

A: Solution

Q: If A,B are two independent event in a sample space , if P(A) = 0.7,P(B) =0.6. Find PAU B) Select…

A: According to the provided information, we have A and B are two independent…

Q: Let A and B be events in a sample space S such that P(A)= .4, P(B)= .5, and P(ANB) = .3. Find:…

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Q: If A and B are events in a sample space S, then P(AUBC) is equal to P(AnB) +P(A°) P(AnB) +P(A°)…

A:

Q: If A,B are two independent event in a sample space , if P(A) = 0.7, P(B) =0.6. Find P(AU B) Select…

A: According to the given information, we have P(A¯)=0.7P(B¯)=0.6

Q: Let A and B be two events in the sample space ( S ) , with P ( A ) = 0.72 , P ( B ) = 0.68 and , P (…

A: we have given that  A and B two events  with P ( A ) = 0.72 , P ( B ) = 0.68 and , P ( A U B ) =…

Q: If A and B are two independent events in a sample space S, find weather the following statement is…

A: Given that A and B are two independent events This means P(A∩B)=P(A)P(B)

Q: If A and B are two independent events in a sample space S, find weather the following statement is…

A: We know that if two evants A ,B are independentif and only if P(A∩B)=P(A)×P(B)and if A ,B are…

Q: Suppose that A and B be two events defined on a sample space 2 with P(A) = 0.7, P (B|A) = 0.4 and P…

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Q: Let E and F be events defined on the same sample space. Find Pr[F] if it is known that Pr[E = Pr[EU…

A:

Q: If A and B are two independent events in a sample space S, find weather the following statement is…

A: Note: " Since you have asked multiple question, we will solve the first question for you. If you…

Q: Let S be the sample space from an experiment, and let events A and B have the following properties:…

A: A ∩ B = ∅ Thus, P(A ∩ B) = 0    ----(1) Note that P(A) >0 and P(B)>0. Therefore, P(A)P(B)…

Q: 2.3 Let A and B be two events af the same sample space. If A and B are independent and P(A) = 0.5…

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Q: Refer to the Venn diagram for events a abs B in an equally likely sample space S. Find the indicated…

A:

Q: 1) Let A and B be events on the same sample space, with P (A) = 0.6 and P (B) = 0.7. Can these two…

A: Given: P (A) = 0.6 and P (B) = 0.7

Q: 2. Give the complement of the event under the given sample space S = {30, 31, 32, 33, 34, 35, 36,…

A: Given information: 2. The sample space S is defined as: S=30,31,32,33,34,35,36,37,38,39 The two…

Q: Let A and B be two events in the sample space ( S ) , with P ( A ) = 0.72 , P ( B ) = 0.68 and , P (…

A: We have given that,  A and B are two events from sample space S,  P(A) = 0.72, P(B) = 0.68 and…

Q: Let A and B be two independent events of a sample space. If P(A)=pa and P(B)=pb, then the…

A: The probability that at most one of them occurs is,

Addition Rule of Probability

It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.

Expected Value

When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).

Probability Distributions

Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.

Basic Probability

The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.