Given P(A) = 0.6 and P(B) = 0.8, do the following. (a) If A and B are independent events, compute P(A and B). (b) If P(A | B) = 0.5, compute P(A and B).

Q: U and V are mutually exclusive events. P(U) = 0.33; P(V) = 0.54. Find: a. P(U and V) = b. P(U|V) =…

A: It is given that P(U)=0.33 and P(V)=0.54.

Q: The probability that event A or event B will occur is

A: Given that  The probability that event A or event B will occur is P(A or B)=P(A)+P(B)−P(A or B).…

Q: If ​P(A∪​B)=0.8​, ​P(A)=0.2​, and ​P(A∩​B)=0.15​, find​ P(B). Assume that A and B are events.

A: Given information- We have given that A and B are events. P(A∪​B)=0.8​, ​P(A)=0.2​, P(A∩​B)=0.15. We…

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: Sarah has two tests at school next week, a math test and a physics test. Let A represent the event…

A: According to the provided information, P(A)=0.30 and P(A AND B)=0.21,

Q: Let A and B be events with =P(A)= 0.2, P(B)=, 0.88, and P(B|A)=0.6.…

A:

Q: If A and B are independent events P(A) = 0.24 and P(A or B) =0.68 Find P(B)

A: P(A)=0.24, P(A or B)=0.68

Q: assume that Pr[A∪B]=0.6 and Pr[A]=0.2 (1) What is Pr[B] if A and B are independent events?

A: Since A and B are independent event, so pr(A∩B)= pr(A)pr(B).

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: A and B are two events such that P(A) = 0.4, P(B) = 0.8, and P(A and B) = 0.2.  Find P(A|B). Select…

A: P(A) = 0.4, P(B) = 0.8, and P(A and B) = 0.2.

Q: If A and B are independent events with P(A)=0.1 and P(B)=0.7, find P(A AND B).

A: Introduction: Suppose X and Y are two events, with respective probabilities P (X) and P (Y). Denote…

Q: Suppose A = = the event that you get 8 hours of sleep, and B = the event that you exercis If P(A) =…

A: We have given that  P(A) = 0.26 P(B) = 0.37 P(AB) = P( A and B ) = 0.11   Conditional probability…

Q: To compute  P(A and B)  means that we wish to find the probability that both A happened and B…

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

Q: Suppose that A and B are events such that P(A) = 2/7 and P(A&B) = 3/25. Determine P(B| A).

A:

Q: you are givin the information that P(A) = 30 and P(B) = 0.40. Do you have enough information to…

A:

Q: If A and B are independent events with P(A)=0.9 and P(B)=0.6, find P(A AND B).

A: Given that A and B are independent events. P(A) = 0.9 P(B) = 0.6

Q: Suppose that A and B are independent events such that P (4)=0.40 and P(B)-0.70. Find P(ANB) and P…

A: We have given that A and B are independent events.

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.