Two gas stations are located in a certain intersection. Each one has six gas pumps. Consider an experiment in which the number of pumps in use at a particular time of a day. (1) Let A denote that event that the number of pumps in use is the same for both stations. List the outcomes in A. (2) Let B denote that event that the total number of pumps in use is five. List the outcomes in B.

Q: Suppose that A and B are independent events such that P(A) = 5/8 and P(B) = 4/7. Find P(A&B).

A:

Q: A and B are two events. If P(A) = 0.20. P(B) = 0.31. P(A/B) = 0.62. Find P(A and B)?

A: Answer: From the given data, P(A) = 0.20 P(B) = 0.31 P(A|B) = 0.62

Q: You randomly select two poker chips from a bag containing 7 poker chips: 3 red, 2 green, 1 blue and…

A: 3 red  2 green 1 blue 1 white _____________ 7 total chips   event A : green chip selected event B:…

Q: If the P(A) = 0.43, P( A or B) = 0.87, given that events A and B are mutually exclusive events then…

A: Given, P(A) = 0.43 P( A or B) = 0.87 Since events, A and B are mutually exclusive events P(A and B)…

Q: Two dice are rolled. Each comes up with a number between 1 and 6. Let A be the event that the number…

A: Two dice are rolled.Sample space S={ (1,1) (1,2) (1,3) (1,4) (1,5) (1,6) (2,1) (2,2) (2,3) (2,4)…

Q: Suppose that A and B are events such that P(A) = 0.84,P(B) = 0.46, and P(A&B) = 0.38. Determine…

A:

Q: Consider two events, A and B, such that P(A) = 0.6, P(B) = 0.7 and P(A intersection B) = 0.4. What…

A: There are two events A and B, and their probabilities are shown below;.

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: Suppose that E and F are two events and that P(E) = 0.5 and P(F|E) = 0.2. What is P(E and F)? P(E…

A: GivenP(E)=0.5P(F|E)=0.2

Q: 3.if A and B are two events such that P(AUB) = P(ANB) = and P(A) = 3, then P (B) is equal to a. 1/3…

A: The question is about probability.Given probabilities are as follows :

Q: A bag contains 10 red, 12 white and 8 blue balls. Three balls are drawn at random from this bag.…

A:

Q: Let A and B be two disjoint events such that P(A) = 0.09 and P(B) = 0.56. What is P(A or B)?

A: A and B are disjoint events.  P(A) =- 0.09 P(B) = 0.56 P( A or B) = ?

Q: You are given two events C and B. You want to determine if the events are mutually exclusive…

A: Determine whether the events C and B are mutually exclusive or not.   The correct option is…

Q: Given P(A) = 0.10, P(B) = 0.36, P(C) = 0.27 and that events A, B, and C are independent, what is…

A: Independent Events:   Any three events A , B and C are said to independent if the occurrence of the…

Q: If B CA and A and B are two events such that P (A) = 3 P (B) and A UB = S find P (B) ?

A: Answer: For the given data,

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

A:

Q: Suppose that A and B are two events for which P(A) = 0.29, P(B) = 0.74, and P(B|A) = 0.42 Find each…

A:

Q: Suppose that we have two events, A and B, with P(A)=0.60,P(B)=0.70, and P(A∩B)=0.40 a. Find P(A∣B)…

A:

Q: Q. 2 If A and B are two events associated with an experiment and P(A) = p. Find the choice of p for…

A:

Q: A section of an electrical circuit has two relays, numbered 1 and 2, operating in parallel. The…

A: Solution

Q: When A and B are any two events such that P(A) = 0.55, P(B) = 0.41 and P(AUB) = 0.4 then P(AN B) =…

A: We have to find given probability.

Q: 1. Roll a die twice. Consider the following events. E1: Roll three dots first. E2: Roll one dot…

A: Ans - Given, Rolling a dice twice  then                    Sample space (S) = {(1,1), (1,2), (1,3),…

Q: If A and B are two events such that P (A or B) =2/3 , P(ABC)=1/3 and P(A/B)= 1/6. Find P(A). Select…

A: For two events A and B,

Q: If A and B are two events such that P (A or B) =2/3 , P(A N BC )=1/3 and P(A/B)= 1/6. Find P(AC or…

A:

Q: Suppose that A and B are two independent events for which P(A)=0.32 and P(B)=0.7. Find each of the…

A:

Q: A concession stand at a movie theater offers soda and popcorn for sale. A survey shows that that 50%…

A: Given that  A=purchase soda B=purchase popcorn  P(A)=50% , P(B)=45% , P(A and B)=25%

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: H. Suppose that P ( A̅ ∩ B) = 0.3, P ( A̅ ∩ B̅) = 0.15, and P(A|B) = 0.5. Find P(A), P(A ∩B ).…

A: As per our guidelines we are suppose to answer only one question. P(A¯∩B)=0.3P(A¯∩B¯)=0.15P(A|…

Q: A director needs 5 students to fill roles in her performance. 8 students, including Justin and Emma,…

A: In the world of theater, casting is a critical process that determines the individuals who will…

Q: Suppose that A and B are two independent events for which P(A)=0.34 and P(B)=0.57. Find each of the…

A: Probability quantifies the chances of happening an event. The probability values always lie in the…

Q: An experiment consists of casting a pair of dice and observing the number that falls uppermost on…

A: Let the sample space for casting a pair of dice is, P(two…

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.