Which of the following expressions must be true if events A and B are independent? Choose from the answer options below.  A.  P(A|B)P(A)=P(A)P(B) B, ) None of the other options are correct C)  P(B|A)=P(A∩B)/P(B) D) P(A|B)=P(B|A)

Q: A group of students conducted a survey about a person's drink preference. It was found that out of…

A:

Q: The Boolean sum of the variables z, y and z or their complements, that has the value 0 if and only…

A: Given x=0y=1z=1 Thus yc = 0zc = 0 We know that  a+b = 0 if and only if both a and b are zero

Q: given n (A⋂B) = 18, n (A) = 3, n (B) and n (A⋂B) = 2.Find n (B) and the number of subsets of set B

A: Solution

Q: Suppose a class of 5 boys and 6 girls are to attend a theatrical performance, and the teacher…

A:

Q: uate: S dz V4z+z? zp=

A:

Q: Colors of Balls Taken Ball:Color Number of Times Red 13 Green 7 Blue 14 Yellow 21 Which of these…

A:

Q: If p: Roger likes Vanessa and q: Vanessa likes Roger, then ∼(p∧q) is ?

A: p: Roger likes Vanessa and q: Vanessa likes Roger "∼" Symbol represent 'negation' ( Or not) "∧"…

Q: 200 ADD NOTE QUESTION GU It is three times as likely to be yellow as it is to be green. It is three…

A:

Q: For any set of numbers, one-half of them is less than mean, is it "True" or "False"? O True O False

A: Mean:  Mean is the arithmetic average of a data set. Set of numbers:  set of numbers can be positive…

Q: Say True or False and justify your answer. P(A∪B)⊆P(A)∪P(B)

A:

Q: Is the following statement true or false? {0} ⊂ {0}

A: given that                                                    {0}⊂{0} we have to check is the…

Q: If U is the set of all multiples of 3 less than 20, and M={3,12,18}, find Mc (the complement of M).…

A:

Q: Prove or disprove: For all sets A, B, we must have 24A2(AAB) = 2B.

A: Given, 2A∆2A∆B

Q: Suppose P(E) = 0.74, P(F) = 0.4, and P(E´∩F) = 0.49. Find P(E´∪F). Note the complement symbols.…

A:

Q: Simplify and identify any p-values for which the expression is undefined... p* - 2р - 15 p + 3

A:

Q: Let A, B, C, D be sets. (ANB)x(CND)=(AXC)n(BxD). True. False.

A: Use the basic properties of intersection and cartesian product to prove the given relation.

Q: Prove. all sets A,B and C, (a) (A-B)- C = CA-C)-B disprove each of the following for or

A: We Know that A - B means elements of A which are not the elements of B. i.e.      A - B = {x : x ∈ A…

Q: Write a single statement that displays a number at random based on the specified set: (a) 2 4 6 8 10…

A:

Q: Disprove: For all sets A, B, C, and D, (AUC) × (BUD) C (A × B) U (C × D).

A:

Q: Evaluate (-p a (p→ q)) → ¬q = T O False O True

A: We will find out the required truth value.

Q: If A ,B are independent then P(ANB) = P(A)P(B) Select one: O True O False

A: From the provided information, The events A and B are independent.

Q: Find n(A) for the set. A= {5, 5, 6, 6, 9, 9} O A. n(A) = 10 O B. n(A) = 3 O C. n(A)= 6 O D. n(A) = 5

A: We have to find nA for the set, A=5, 5, 6, 6,.....,9, 9 nA is the number of elements present in the…

Q: Given P(A) = 0.30, P(B) = 0.46 , and P(A and B) = 0.31 is P(AorB) ?

A: Given that, P(A)= 0.30 and P(B)=0.46 PA and B=PA∩B=0.31 From the probability theory, PA or B=PA∪B…

Q: The contrapositive of the implication p + q is O -4 + -p OpA -g

A: A contrapositive statement occurs when you switch the hypothesis and the conclusion in a statement,…

Q: ition 1.3 3 4 う 3. 2 2. 2.

A: Use the table to evaluate each expression. a) f(g(1)) b) g(f(1)) c) f(f(1)) d) g(g(1)) e) (g • f)(3)…

Q: Show that if A and B are sets, then P(A) u P(B) c P(A u B), where P(A) denotes the power set of A

A:

Q: a. What is P(A|B)? P(A and B)/P(B)=. b. What is P(B|A)? P(A and B)/P(A)= Are A and B independent? C.…

A: a) The required probability is calculated as follows: P(A|B) = P(A and B)/P(B)             =…

Q: Q1. How many different subsets are in cach of the following sets? Justify your answer. (a) (0} (b)…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Let A = {3, 4, 5, 6, 9}, Write down each of the following sets. (a) An B. (b) {b-2: be B and b+ 2 &…

A:

Q: Let R = {(a, b), (b, a), (a, c), (c, d), (d, a)} a. Is (a, c) E R³? b. Is (a, a) E R²? c. Is (c, c)…

A:

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.