470 None 50 420 390 Mild 330 60 140 Strong 20 120 1000 Column Total 500 500 Let's use the following notation for the various events: W= washing oil off within 5 minute, A = M = mild reaction, S = strong reaction. Find the following probabilities for a person selected at random from this sample of 1000 subjects. (a) P(N), P(M), P(S) (b) P(N | W), P(S I W) (c) P(N|A), P(SLA) washing oil off after 5 minutes, N = no reaction,

Q: Suppose A and B are two events, P(A)=0.38, P(B)=0.42 and P(A and B )=0.26 Find the P(B|A) Round…

A: Answer: From the given data, P(A) = 0.38 P(B) = 0.42 P(A and B) = 0.26

Q: A and B are two events. P(A) = 0.27, P(B) = 0.32, P(A and B) = 0.14. Calculate P(B | A')?…

A: Answer: From the given data, P(A) = 0.27 P(B) = 0.32 P(A and B) = 0.14

Q: Suppose that events E and F are independent with P(E)= 0.6 and P(F) = 0.8 What is P(E and F)? round…

A: Answer: From the given data, P(E) = 0.6 P(F) = 0.8 The events E and F are independent,

Q: If A and B are independent events such that P(A) = 0.2600 and P(A N B) = 0.2054. Find P(B). %3D

A:

Q: If A and B are independent events, P(A)=0.25, and P(B)=0.79, what is P(B|A)?

A:

Q: P(A) =0.3 and P(A or B) =0.7, then what is P(B)  if events A and B are independent events?

A:

Q: s some event, if P(A) = 0.91 , what is the value of P(A)?

A: Given P(A) = 0.91

Q: If A and B are independent events with P(A) = 0.6 and P(B) = 0.3. Find the P(A/B) Select one: a. 0.4…

A: Given,P(A)=0.6P(B)=0.3and A , B are independent events.

Q: Two events A and B are such that P(A) = 0.19, P(AN B)= 0.15, P(A or B ) = 0.99. Find P(A N BC).…

A: The given events and their probabilities are as follows: P(A)=0.1 PA∩B=0.15 PA∪B=0.99 Need to find…

Q: Which of the following events are independent, given P(A),P(B), and P(A and B)? A. P(A) = 0.3; P(B)…

A: We have to check

Q: If A and B are events with P(A)=0.6, P(A OR B)=0.98, P(A AND B)=0.02, find P(B).

A:

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: TRUE or FALSE  For events A and B in a sample space, P(A|B) + P(A|Bc) = P(B).

A: Introduction: Suppose A and B are two events of interest in a sample space, with respective…

Q: Suppose A and B are independent events. If P(A) = 0.45 and P(B) = 0.35, find each of the following:…

A:

Q: If A and B are independent events, P(A)=0.22, and P(B)=0.71, what is P(B|A)?

A: Given: A and B are independent P(A)=0.22 P(B)=0.71   A and B are independent means that occurring of…

Q: Let A, B be two events such that p(An B) = 0.4, P(B n A) = 0.1 and p(An B) = 0.6. Find p(A) %3D %3D…

A: P(A∩B¯) = P(only A) = 0.4 P(B∩A¯) = P(only B) = 0.1 PA∩B¯ = 1 - P(A∩B) P(A∩B)  = 1 - 0.6 = 0.4

Q: a) Two events, A and B, are such that P(AuB) = 0.86, P(B) = 0.72 and P(A) = 0.64. Determine (i) P…

A: We calculate  probability of  given events

Q: te: Please don't write your answers in a paper, I can't understand handwritten well.

A: Let us assume that a 6 sided die is tossed Then sample space is S={1,2,3,4,5,6}

Q: If A and B are independent events with P(A) = 0.6 and P(B) = 0.3. Find the P(A/B) Select one: O a.…

A:

Q: Events A and event B are mutually exclusive, P(A)=0.5 and P(B)=0.3 Calculate the following,…

A: Answer: From the given data, P(A) = 0.5 P(B) = 0.3 Events A and B are mutually exclusive,

Q: If A and B as shown below are two dependent events, what is P(A or B)? P(A) = , P (B) = , P(A and B)…

A:

Q: Given two independent events, X and Y, such that P(X) = 0.30 and P(X AND Y) = 0.12, what is the…

A: Given There are 2 independents events X and Y. PX=0.30P(X and Y)=0.12

Q: Let A and B two events with P(A) =0.25 and P(B) =0.45 and P(A n B) = 0.1 then P(Ā N B) = 0.35. O…

A: The given probabilities are PA=0.25,PB=0.45,PA∩B=0.1. Now, PA¯∩B=PB-PA∩B=0.45-0.10=0.35=True Thus,…

Q: If A and B are independent events with P(A) = 0.25 and P(B) = 0.60,then P(A|B) is?

A: Given: A and B are independent events. P(A)=0.25P(B)=0.6 The objective is to find P(AB).

Q: If A and B are independent events, P(A)=0.25, and P(B)=0.85, what is P(B|A)?

A: Given that, A and B are independent events. P(A) = 0.25 P(B) = 0.85

Q: Suppose X and Y are events in a sample space such that P(X|Y) = 1 3 and P(Y) = What is P(XY)?

A: X and Y are the events in a sample space such that, P(X|Y)=1/3 P(Y)=1/5 To find: P(X and Y)

Q: 0.13, find P(B). If A and B are events with P(A) = 0.7, P(A OR B) =0.77, and P(A AND B) %3D %3D

A: Given information: Two events A and B. The probability of occurrence of event A, P(A)=0.7. The…

Q: If A and B are independent events, P(A)=0.18, and P(B)=0.79, what is P(B|A)

A: Given that; P(A) = 0.18 P(B) = 0.79 If A and B are independent events,

Q: A and B are both events in sample space S.   P(A)=0.4 P(B)=0.3 P(A and B) =0.2   What's the…

A: A and B are both events in sample space S. Given, P(A)=0.4 P(B)=0.3 P(A and B) =0.2

Q: Suppose that events E and F are independent with P(E)=0.65 and P(F)=0.72 What is P(E andF)? Round…

A: P(E)=0.65 P(F)=0.72 The events E and F are independent .

Q: Let E and F be two events of an experiment where P(E) = 0.45, P(F) = 0.12 and P(EnF) = 0.04. Then…

A:

Q: Suppose that events E and F are independent with P(E)= 0.5 and P(F) = 0.7 What is P( E and F )…

A: Answer: From the given data, Suppose that events E and F are independent  P(E) = 0.5 P(F) = 0.7

Q: Suppose that E and F are two events and that P(E)=0.8 and P(F|E)=0.5. What is P(E and F)​?

A: Given data,  P(E)=0.8  P(F|E)=0.5 P(E and F)​=?

Q: = 0.2 and P(B) = 0.4, then %3D If A and B are two independent events where P(A) P(AN B) = O 0.2 O…

A:

Q: Given P(A) = 0.076, P(B) = 0.184, and P(C) = 0.159, and that events A, B, and C are mutually…

A: Solution: Mutually exclusive events: Two events A, B and C are said to be mutually exclusive when…

Q: Suppose A and B are events in a sample space S, and P(A|B) 3 and P(B) 4 What is P(An B)? !! %3D…

A: Here given that P(A|B)=3/7 and P(B)=4/5. We need to find Probability of Intersection of A and B.

Q: A and B are two events such that P(A) = 0.4 and P(An B) = 0.2 Then P(An B) is equal to O 0.8 O 0.6…

A:

Q: Two events A and B are such that P(A /B) = 0.5, P(A N B)= 0.15,P(A or B ) = 0.65. Find P(ACN B©).…

A: From the provided information, P (A|B) = 0.5, P (A Ո B) = 0.15, P (A or B) = 0.65

Q: If A and B are two events with P(A) = 0.51, P(B) = 0.23 and P( A and B) = 0.13 What is P(B | A)?

A: A and B are two events with P(A) = 0.51, P(B) = 0.23 and P( A and B) = 0.13

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.