Suppose that you have 4 green cards and 5 yellow cards. The cards are well shuffled. You randomly draw two cards without replacement.  G1 = the first card drawn is green G2 = the second card drawn is green a.  P(G1 and G2) = b.  P(At least 1 green) = c.  P(G2|G1) = d.  Are G1 and G2 independent?  They are independent events They are dependent events

Q: Suppose that E and F are two events and that P(E and F) = 0.3 and P(E)=0.8. What is P(FIE)? P(FIE)=…

A: given data  P(E and F) = 0.3 P(E) = 0.8 P(F|E) = ?

Q: A group of students at a high school took a standardized test. The number of students who passed or…

A:

Q: 2. Let A and B be events with P(A) = 0.5 and P(AnB") = 0.4. For what value of P(B) will A and B be…

A:

Q: Suppose that A, B are two independent events, with P(A) = 0.3 and P(B) = 0.4. Find P(A and B)

A:

Q: Given P(A) = 0.3 and P(B) = 0.4; if A and B are mutually exclusive events, compute P(A or B)

A:

Q: Suppose that A and B are independent events with: P(A)= 0.4 P(B)= 0.7 Calculate: P( A U B)

A: The union probability for any two events A and B is defined as P(A ∪ B) = P(A)  + P(B) – P(A ∩ B).

Q: Suppose that you have 8 green cards and 5 yellow cards. The cards are well shuffled. You randomly…

A: We have 8 green cards and 5 yellow cards. Two cards are drawn at random G1 = the first card drawn is…

Q: If A and B are mutually exclusive events with P (A) = 0.30 and P (B) = 0.40, then P (A or B) is:

A: GivenP(A)=0.30P(B)=0.40A and B are mutually exclusive

Q: If A and B are independent events with P(A) = 0.35 and P(B) = 0.20, then, P(A ∪ B) =

A: We have given that two events A and B are independent. P(A) = 0.35 P(B) = 0.20 We have to find P (A…

Q: Suppose that A and B are mutually exclusive events with P(B) = 0.224 and ?(?∪?) P(A∪B)= 0.673.…

A: From the provided information, P (B) = 0.224 and P (A U B) = 0.673 The events A and B 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)?

A:

Q: Suppose that A,B, and C are independent events such that P(A) = 0.8,P(B) = 0.5, and P(C) = 0.3. Find…

A: The Special Multiplication Rule

Q: (a) For two events, A and B, P(A) = 0.5, P(B) = 0.4, and P(ATB) = 0.2. Compute P(A|B) and P(B|A).…

A: Solution. Dear student as per guidelines we answer the first question only when multiple different…

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

A: Solution: From the given information, E and F are independent events, P(E) = 0.2 and P(F)= 0.2.

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: Let A and B be events with P(A) = 0.8 and P(A ∩ B) = 0.2. For what value of P(B) will A and B be…

A: Given,  P(A) = 0.8  P(A ∩ B) = 0.2 P(B)=?

Q: Consider two independent events A and B.Suppose it is known that P(A)=0.27 and P(A or B)=0.5474.…

A:

Q: Suppose A and B are dependent events and P(B | A)=0.4, P(ANB)=0.1, P(B')=0.62. Find P(A U B).

A: Consider that A and B are two dependent events.

Q: Consider randomly selecting a student at a large university, and let A be the event that the…

A:

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

A:

Q: Let A and B be two events such that P(A) = 0.6 and P(B) = 0.4. 1) Is P(C) = P(C given A) x P(A) +…

A: 1) Consider, P(C|A)P(A)+P(C|B)P(B)=P(C and A)P(A)P(A)+P(C and B)P(B)P(B)…

Q: When looking at the association between the events "owns a car" and "owns a pet," if the events are…

A: use the formula for the probability of an independent event

Q: Suppose A and B are mutually exclusive events with P(A) - 0.25 and P(B) = 0.25. Find the following…

A: For Mutually exclusive events, P(A U B) = P(A) + P(B)               =0.25 + 0.25               =0.5…

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: E and F are independent events. Suppose that Pr[E|F]=0.5 and Pr[F|E]=0.4. Answer the following…

A:

Q: A dice is rolled once. Let E be the event of an even number coming up, O the event of an odd number…

A: From the given information we want to know the event are independent or not.

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: Consider, If A and B are independent events, P(A)=0.26 and P(B)=0.76, Find: 1. P(A n B) 2. P(A| B)…

A: Given: P(A)=0.26  P(B)=0.76

Q: E. If P(A)=0.8, P(B)=0.5, and P(AUB)=0.9, are A and B independent events? Why or why not

A: P(A) = 0.8 P(B) = 0.5 P(A U B) = 0.9   P(A ∩B) = P(A) + P(B) - P(A ∪B) P(A ∩B) =0.8 + 0.5 - 0.9P(A…

Q: Suppose that you have 4 green cards and 5 yellow cards. The cards are well shuffled. You randomly…

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

Q: If A and B are independent events with P(A)=0.9 and P(B)=0.8, find P(A AND B).

A: It is given that , A and B are the two independent events & their probabilities is P(A) = 0.9…

Q: If A and B are two independent events with P(A) = 0.15 and P(B) = 0.4, then P(AUB) is

A:

Q: If P(A) = 0.2, P(B) = 0.4, and A and B are independent events, find P(A and B)

A: Solution: From the given information, P(A)=0.2 and P(B)=0.4.

Q: When looking at the association between the events "owns a car" and "owns a pet," if the events are…

A: We have to check

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: Let A and B be events with these properties: 0 < P(B) < 1 and P(A|B) = P(A|B^c) = 1/3.(a) Is…

A:

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: If A and B are independent events and P(a)=0.6 and P(b)=0.3, what is P(a^c U b^c)?

A:

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 A and B are independent events with P(A) = 0.2 and P(B) = 0.6, then P(A U B) = 0.80 0.12 0.72…

A: Solution

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: Suppose A and B are two events with P(A)=.35 and P(B) =.6. Find P(A or B) assuming A and B are…

A: Hey there! Thank you for posting the question. Since there are multiple questions posted, we will…

Q: Suppose A and B are events such that P(A) = 0.6 P(B)= 0.7 and P(A or B) = 0.8 What’s P(A) with a…

A: Given, Suppose A and B are events such that P(A) = 0.6 P(B)= 0.7 and P(A or B) = 0.8. That is,…

Q: Suppose A and B are events with P(A) = 0.3, P(B) = 0.65, and P(B|A) = 0.6. Find the value of P(A or…

A:

Q: If A and B are independent events with P(A)=0.6 and P(B)=0.2, find P(A AND B).

A: P(A) = 0.6 P(B) = 0.2

Q: Suppose that A and B are independent events with P(A) = .40 and P(B) = .70, then P (B'/A') is

A: Given information- P(A) = .40 P(B) = .70 We have to find P (B'/A'). We know that- P(A’) = 1 - P(A)…

Q: IHA and B are mutually exclusive events with P(A) = 0.40 and P(B) = 0.20, then PAIB) is: 0.5 0.4…

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

Q: If A and B are independent events, with P(A) = 0.2 and P(B) = 0.3,then P(A and B) is?

A: Given, A and B are independent events. P(A)=0.2 P(B)=0.3

Q: Q2/ An urn contains 5 red, 6 blue, and 8 green balls. If a set of 3 balls is randomly selected, what…

A: It is given that Number of red balls = 5 Number of blue balls = 6 Number of green balls = 8 Total =…

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.