A. If Events E and F are disjoint events, then P (F | E) = B. For events E and F, the probability P (E) -P (ENF) is equal to the probability C. If E and F are independent events, then P (F | E) =.. D. For events E and F, if Ec F then P (F | E) = ... ...... select 1. P(ENF) select 2. 0 select 3. P(F) select v 4.1

Q: nsider event A and event B, if ?(??)=0.46 and ?(?)=0.58, If ?( ?∪ ?)=0.8. a. Find ?(?∩?). b. Could…

A: It is given that the There are two events A and B such that  P(A) = 0.46, P(B) = 0.58, P(A∪ B) = 0.8…

Q: Suppose that events E and F are​ independent, ​P(E)=0.4​, and ​P(F)=0.6. What is the P(E and F)​?…

A: Given that, Events E and F are independent, and P(E) = 0.4 P(F) = 0.6

Q: Given P(A and B) = 0.16, P(A) = 0.20, and P(B) = 0.80 are events A and B independent or dependent?

A: GivenP(A)=0.20P(B)=0.80P(A∩B)=0.16

Q: If A,B,C are mutually exclusive events with PĀ) = 0.45, P(B) = 0.36, then P(AN B) = a. 0.91 O b.…

A: PA=0.45 PB=0.36

Q: If A and B are independent events with P(A) = 0.5 and P(B) = 0.5, then P(A ∩ B) is   Question 9…

A: GivenA and B are independent events P(A)=0.5P(B)=0.5

Q: Given P(A) = 0.47, P(B) = 0.41, and P(A or B) = 0.88, are events A and B mutually exclusive?…

A: Events A and B are mutually  exclusive when  Hence, Event A and B are mutually exclusive.

Q: Suppose events A, B and C are independent and P(A)= 1/4 P(B)= 1/2 P(C)= 1/3 Find the…

A: Given Information: A, B and C are Independent events. P(A) = 14 P(B) = 12 P(C) = 13   To find the…

Q: Given P(A and B) = 0.07, P(A) = 0.75, and P(B) = 0.63 are events A and B independent or dependent?…

A:

Q: If A and B are events with P(A)=0.4, P(A or B)=0.53, and P(A and B)=0.07, find P(B)

A:

Q: Suppose events A, B, and C are independent and P(A) =  1 4    P(B) =  1 5     P(C) =  1 8 Find the…

A: From the provided information, P (A) = 1/4, P (B) = 1/5 and P (C) = 1/8

Q: Given P(A) = 0.62, P(B) = 0.78, P(C) = 0.61 and that events A, B, and C are independent, what is…

A:

Q: If E and F are two disjoint events in S with P(E) = 0.41 and P(F) = 0.26, find P(E U F), P(E©), P(E…

A:

Q: Suppose events A and B are NOT disjoint, and that P(A) = 0.3 and P(B) = 0.15. What is P(A or B)? 2.…

A: Disjoint events:   Let A and B be any two events, if the events A and B are mutually exclusive or…

Q: Given that P(A) = 0.47, P(B) = 0.07, and P(A and B) = 0.0329, are events A and B independent? O Yes,…

A: No. They are not independent.

Q: Given P(A) = 0.51, P(B) = 0.79, and P(A or B) = 0.66, are events A and B mutually exclusive?

A:

Q: If A and B are independent events with P(A) = 0.5 and P(A ∩ B) = 0.12, then, P(B) = Question 27…

A:

Q: Suppose two events E and F are disjoint.  Which of the following is true? A.) P (E or F) = 1 B.) P…

A: If E and F are disjoint then there is no common area between E and F They roughly look like: So the…

Q: Suppose two events E and F are disjoint.  Which of the following is true?   (1 answer) A. P(E or F)…

A: If two events E and F are disjoint then P(E and F)=0

Q: given p(a)=0.23, P(B)=0.05, P(C)=0.65 and that events A,B and C are independent, What is P(A,B, and…

A: given p(a)=0.23, P(B)=0.05, P(C)=0.65 and that events A,B and C are independent, What is P(A,B, and…

Q: Given P(A) = 0.59, P(B) = 0.51, P(C) = 0.09 and that events A, B, and C are independent, what is…

A:

Q: a)Suppose events E and F are mutually exclusive with P(E)= 0.15 and P(F)= 0.75. (i) What is the…

A: We have given that  P(E)= 0.15 and P(F)= 0.75. IF A and B are mutually exclusive.  P ( A U B ) = 0…

Q: Suppose that event A and Event B are independent events. Which of the following statements is NOT…

A: The theory of probability has its origin in the seventeenth century.The king of France who…

Q: tudent has an American Express card. Suppose that P(A) = 0.6, P(B) = 0.4, and P(A N B) = 0.3,…

A:

Q: Suppose that, for events A and B, P(A)= 0.2, P(B)= 0.85, and P(AandB)= 0.17. (i)    Calculate the…

A:

Q: Consider events C and D, such that P(C′)=0.6, P(D′)=0.4 and P(C∩D)=0.3. Find P(C|D)

A: Given that, P(C′)=0.6 P(D′)=0.4 P(C∩D)=0.3

Q: If A, B, and C are mutually exclusive events, with P(A) = 0.2, P(B) = 0.3, and P(C) = 0.4, what is…

A: As per our guidelines we are suppose to do only one questionGivenA,B and C are mutually…

Q: Let A, B, and C be independent events with P(A)= 0.8, P(B)= 0.3, and P(C)=0.4 Find P(A and B and C).…

A: given A, B, and C be independent events  P(A)= 0.8, P(B)= 0.3, and P(C)=0.4 P(A and B and C ) = ?

Q: Given P(A)=0.31, P(B)=0.49 and P(A or B)=0.78, are events A and B mutually exclusive

A: According to the given information, we have P(A) = 0.31 P(B) = 0.49 P(A or B) = 0.78

Q: Suppose A and B are two independent events, with P(A) = 0.20 and P(B) = 0.60. What is P(B|A). a)…

A: Given : Suppose A and B are two independent events   P(A) = 0.20 P(B) = 0.60

Q: Suppose an event E and its complement E then P(E) +P(E) = 1 P(E) +P(E) =0 P(E) - P(E) =1 P(E) P(E)…

A:

Q: If A,B,C are mutually exclusive events with P(A) =0.25, P(B) = 0.22, P(C) = 0.75 then PAUBUC) O a.…

A: Given, A,B,C are three events with PA¯=0.25,PB¯=0.22,PC=0.75

Q: Suppose E1, E2, E3, E4, and E5 are mutually exclusive and exhaustive events. Let A be an event with…

A: Given:  E1, E2, E3, E4, and E5 are mutually exclusive and exhaustive events. A be an event with P(A)…

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: Given P(A) = 0.82, P(B) = 0.52, P(C) = 0.79 and that events A, B, and C are independent, what is…

A: Obtain the probability that the three events A, B and C are independent events. The probability that…

Q: If two events, Event A with probability P(A) and Event B with probability P(B) are independent, then…

A: Given that two events, Event A with probability P(A) and Event B with probability P(B) are…

Q: Suppose A and B are independent events with P(A) = .6 and P(B) .8. Find (a) P(AU B), (b) P(AU B“),…

A: Given,P(A)=0.6P(B)=0.8and A, B are independent events

Q: Suppose A, B, and C are events so that P ( A ) = 0.2 , P ( B ) = 0.5 , P ( C ) = 0.3 , P ( A ∩ B )…

A: P(B)×P(C)=0.5×0.3=0.15=P(B∩C) Since we get P(B∩C)=P(B)×P(C), so B and C are independent.

Q: If A and B are independent events associated with an experiment P(A)=0.4, P(AUB)=0.7, then the…

A:

Q: If A and B are events with P(A)=0.7, P(A OR B)=0.89, and P(A AND B)=0.01, find P(B).

A: Solution-: Given: P(A)=0.7,P(A OR B)=0.89, P(A AND B)=0.01  We find P(B)=?

Q: Given P(A) = 0.78, P(B) = 0.49, P(C) = 0.45 and that events A, B, and C are independent, what is…

A: Given, P(A) = 0.78 P(B) = 0.49 P(C) = 0.45  that events A, B, and C are independent.       To find,…

Q: Given P(A) = 0.27, P(B) = 0.19, and P(A or B) = 0.46, are events A and B mutually exclusive

A: Given,  P(A) = 0.27 P(B) = 0.19 P(A or B) = 0.46

Q: If A and B are independant events with P(A) = 0.295, P(B) = 0.32, then P(A | B) =

A: It is given that A and B are independent. P(A) = 0.295, P(B) = 0.32

Q: Let E and F be two events and suppose P(E) = 0.48, P(F) = 0.55, and P(E F) = 0.74. Find P(E | F).

A: According to the provided information,  P(E) = 0.48, P(F) = 0.55, and P(E⋂F) = 0.74

Q: Given P(A) = 0.21, P(B) = 0.99, P(C) = 0.31 and that events A, B, and C are independent, what is…

A: We have given that  P(A) = 0.21, P(B) = 0.99, P(C) = 0.31 And events A, B and C are independent.

Q: Given P(A) = 0.88, P(B) = 0.97, P(C) = 0.90 and that events A, B, and C are independent, what is…

A: Solution: From the given information, P(A)=0.88, P(B)=0.97 and P(C)=0.90. Here, the events A, B and…

Q: If E and F are two disjoint events in S with P(E) = 0.23 and P(F) = 0.6, find P(E ∪ F), P(EC), P(E ∩…

A: From the question, it is given that E and F are two disjoint events in S that is both events are…

Q: 11. Given P(A) = 0.52, P(B) = 0.87, P(C) = 0.06 and that events A, B, and C are independent, what is…

A: It is mentioned that the events A, B and C are independent. The probabilities are provided as; P(A)…

Q: Given P(A)=0.37, P(B)=0.38, and P(A or B)=0.27, are events A and B mutually exclusive?

A: If A and B are mutually exclusive then P(A or B) = P(A) + P(B) Here, P(A or B) = 0.27 and P(A) +…

Q: Given P(A and B) = 0.12, P(A) = 0.58, and P(B) = 0.44 are events A and B independent or dependent?

A: Two events A and B are said to be independent if P(A and B)=P(A)×P(B)

Q: and ?B are independent events with ?(?)=0.3P(A)=0.3 and ?(?)=0.4P(B)=0.4, calculate the following:…

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

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.