Leon and Zack are playing a game with dice. Leon rolls the dice first, and Zack rolls second. Are these two events dependent or independent?   dependent independent

Q: Determine whether the statement is true or false. If it is false, rewrite it as a true statement. If…

A: Solution: Mutually exclusive or Disjoint events:  Let A and B are two events of sample space S then…

Q: Two events can be both Dependent and NOT Disjoint. True False

A:

Q: If P(A) > 0, P(B) > 0, and P(A n B) = 0, then the events A and B are independent. true or false?

A: Solution-: If P(A) >0, P(B)>0 and  P(A∩B)=0, then the events A and B are independent. We find…

Q: A and B are two events. If P(A) =0.18, P(B) =0.33, P(A|B) =0.59 Find the P(A and B)

A: P(A) = 0.18 P(B) = 0.33 P(A|B) = 0.59 P(A and B) = ?

Q: What does it mean for three events to be mutually exclusive?

A: Mutually exclusive events Three events are said to be mutually exclusive if they have no element in…

Q: Two events are independent of each other. If the probability of the first is 0.6, and the…

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Q: Suppose you play a game that you can only either win or lose. You win a game with probability 0.538.…

A: It is an application of Binomial distribution .Binomial distribution occurs as a consequence of…

Q: Three players Dan, Emily, and Frank are tossing a biased coin with P(H) = α. They rotate turns…

A: P(H)=α

Q: If two events A and B are independent and you know that P(A) = 0.60, what is the value of P(A | B)?

A: Solution: From the given information, A and B are two independent events and P (A) =0.60.

Q: events A and B are mutually exclusive, then P(A) + P(B) = 0. True or false?

A: Given that  If two event A and B are mutually exclusive.

Q: How do you show that two events are independent?

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

Q: you roll two fair dice. How many ways are there for the sum of the dice to be less than 6?

A: On rolling two dice, let X be the sum of the outcomes. The all possible values of X is…

Q: Roll two fair dice. Is the occurence of an even number on one of them independent of the occurence…

A: The outcome of the die is {1,2,3,4,5,6}.

Q: Two dice, one green and one yellow, are rolled. Find the conditional probability. The sum is 12,…

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Q: Roll a pair of fair dice once. Given that the two numbers that occur are not the same, what is the…

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Q: A game has three possible outcomes: X, Y, or Z. If P(X) = 0.6 and P(Y) = 0.3, what is the…

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Q: The events A and B are mutually exclusive. If P(A) = 0.3 and P(B) = 0.6, what is P(A or B)? O A. 0 O…

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Q: Billy randomly selects a card from a standard deck. The probability of him selecting a king or a…

A: We have given that the Billy randomly selects a card from a standard deck. The probability of him…

Q: If P(A|B) = 0.5 and P(B) = 0.5, then the events A and B are independent. ture or fals

A: Given :  P(A|B) = 0.5 P (B) = 0.5 A and B are independent events. Then,

Q: Two Events A and B are independent if the knowledge that one occurred does not affect the chance of…

A: Note: from the information, it is noted that there is no such event ‘A’. we found only the events…

Q: If two events A and B are independent and you know that P(A) = 0.50, what is the value of P(A | B)?

A: As the events A and B are independent, the probability of occurrence of A is not impacted by the…

Q: The events A and B are mutually exclusive. If P(A) = .33 and P ( B) = .26, what is the P( A or B)

A: Given that  P(A) = .33 and P ( B) = .26

Q: Two buddies, Zeke and Bubba, plan a squirrel-hunting trip. Bubba is a better shot than Zeke. How…

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Q: You roll two dice. What is the probability that one of the numbers is even and the other is odd?

A: There are 6 numbers on a dice, 3 even number and 3 odd numbers on a dice. The probability of getting…

Q: Alice has come to the Carnival and is playing the dart game one time. She gets three tosses. The…

A: Since you have posted multiple sub-parts, we will solve the first three sub-parts for you. To get…

Q: In probability, when two events do not influence each other, they are called ?

A: In probability, when two events do not influence each other, they are called ?

Q: The events A and B are mutually exclusive. If P(A) = .31 and P ( B) = .42, what is the P( A or B)

A: It is given that  P(A) = 0.31 P(B) = 0.42

Q: Problem: Let A and B be events. Is it necessarily true that P(A|B) = P(B|A) ? If so, explain why. If…

A: We have, Let A and B be events. Is it necessarily true that P(A|B) = P(B|A)  ?

Q: The events A and B are mutually exclusive. If P(A) = 0.3 and P(B) = 0.6, what is P(A or B)? O A. 0.9…

A: Given Data: P(A)=0.3 P(B)=0.6   A and B are mutually exclusive events

Q: wo fair dice are rolled. Event A = {the sum on the two dice is more than seven} Event B = {the two…

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Q: The events A and B are mutually exclusive. If ​P(A)=0.6 and ​P(B)=0.2​, what is​ P(A or​ B)?

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Q: About two events A and B, we know that A occurs with 32% probability and B with 15% probability. It…

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Q: Two events A and B are said to be independent if P(A|B) = P(B).  True  False

A: Here use basic of independent event

Q: Two dice, one green and one yellow, are rolled. Find the conditional probability. The sum is 12,…

A: Let 'S' be the sample space representing all the possible outcomes of throwing two dice together.…

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.