A and B are events, neither of which has probability 0. Which conditions below imply that A and B are independent events? Select all that apply. Select 3 correct answer(s) p(A|B) = p(B|A) p(BA) = p(B) p(An B)=p(A) × p(B) p(B|A) = p(A) × p(B)
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- EXERCISE - You go to a market to pick out some gourds to decorate your house for Halloween. The market has a special October deal where you get 3 randomly chosen gourdss for $10. Each gourd can either be an orange pumpkin, a green pumpkin or a squash. The probabilities for picking each one of them are: P(orange pumpkin) = 0.6, P(green pumpkin) = 0.3, and P(squash) = 0.1. A: What is the probability that the first gourd is an orange pumpkin, the second is a green pumpkin, and the third is a squash? B: What is the probability that you get all 3 as orange pumpkins? C: What is the probability that you get no squashes? D: What is the probability that you get at least one orange pumpkin? (ANSWERE USING PYTHON)An Event In the context of the probability experiment just described. Consider the event in which the two numbers on the two dice add to 12. What is the size of this set? Probability of an event (1/2) What is the probability of the event just described? Write your answer as a fraction of integers. For example, if the answer were 17/20 then enter 17/20 with no spaces or other symbols. You may reduce the fraction by cancelling factors common to the numerator and denominator but you do not need to do this. Probability of an event (2/2) What is the probability that at least one 4 appears? Write your answer as a fraction of integers. For example, if the answer were 17/20 then enter 17/20 with no spaces or other symbols. You may reduce the fraction by cancelling factors common to the numerator and denominator but you do not need to do this.Correct answer will be upvoted else Multiple Downvoted. Don't submit random answer. Computer science. You are given a variety of n integers a1, a2, ..., an, and a set b of k unmistakable integers from 1 to n. In one activity, you might pick two integers I and x (1≤i≤n, x can be any integer) and allocate ai:=x. This activity should be possible provided that I doesn't have a place with the set b. Compute the base number of tasks you ought to perform so the cluster an is expanding (that is, a1<a2<a3<⋯<an), or report that it is inconceivable. Input The principal line contains two integers n and k (1≤n≤5⋅105, 0≤k≤n) — the size of the exhibit an and the set b, individually. The subsequent line contains n integers a1, a2, ..., an (1≤ai≤109). Then, at that point, if k≠0, the third line follows, containing k integers b1, b2, ..., bk (1≤b1<b2<⋯<bk≤n). On the off chance that k=0, this line is skipped. Output In case it is difficult to make the exhibit…
- A coin is flipped 8 times in a row (assume all outcomes are equally likely). For each of the following questions, you should write your answer as an expression. Do not give the final numeric value. For example, you should write C(4,2)/24 instead of 0.375. Q1.1 What is the probability that it lands on heads exactly four times?Correct answer will be upvoted else downvoted. Computer science. All arbitrary choices that are made during the title are made similarly plausible and autonomously. For instance, assuming n=4, a=[1,2,4,3], one of the choices for the game (there could be different choices) is: during the main game, the first and fourth players were chosen. The fourth player has more tokens, so he takes the main player's tokens. Presently a=[0,2,4,4]; during the subsequent game, the fourth and third players were chosen. They have similar number of tokens, yet arbitrarily, the third player is the champ. Presently a=[0,2,8,0]; during the third game, the second and third players were chosen. The third player has more tokens, so he requires the second player's tokens. Presently a=[0,0,10,0]; the third player is proclaimed the victor of the title. Title champs will get customized prizes. Consequently, the adjudicators need to know ahead of time which players get an opportunity of winning,…Mastermind is a code-breaking game for two players. In the original real-world game, one player A selects 4 pegs out of 6 colors and puts them in a certain fixed order; multiples of colors are possible (for example, red-green red-green). His opponent B does not know the colors or order but has to find out the secret code. To do so, B makes a series of guesses, each evaluated by the first player. A guess consists of an ordered set of colors which B believes is the code. The first player A evaluates the guess and feeds back to B how many positions and colors are correct. A position is correct ("black") if the guess and the secret code have the same color. Additional colors are correct ("white"), if they are in the guess and the code, but not at the same location. For example1 2 3 4secret: red-green red greenguess: red blue green purpleresults in one correct position ("black = 1") for the red peg at position one and one additional correct color ("white=1") for the green peg in the guess.…
- During the 17th century, gambler de Méré asked Blaise Pascal an explanation for his game losses. His question was solved by Pascal and Fermat, and yielded the foundations of the theory of probability. Gamblers used to bet on the event of getting at least one ace in four rolls of a dice. As a game variation, De Méré proposed to use two die and roll them 24 times with a bet on having at least one double ace. De Méré thought the games were equivalent but he lost consistently. Explain why? Write a simulation program to empirically determine which one dice/two die game is more likely to win.Mastermind is a code-breaking game for two players. In the original real-world game, one player A selects 4 pegs out of 6 colors and puts them in a certain fixed order; multiples of colors are possible (for example, red-green red-green). His opponent B does not know the colors or order but has to find out the secret code. To do so, B makes a series of guesses, each evaluated by the first player. A guess consists of an ordered set of colors which B believes is the code. The first player A evaluates the guess and feeds back to B how many positions and colors are correct. A position is correct ("black") if the guess and the secret code have the same color. Additional colors are correct ("white"), if they are in the guess and the code, but not at the same location. For example1 2 3 4secret: red-green red greenguess: red blue green purpleresults in one correct position ("black = 1") for the red peg at position one and one additional correct color ("white=1") for the green peg in the guess.…Correct answer will be upvoted else Multiple Downvoted. Don't submit random answer. Computer science. every cell of the network contains a non-negative integer. Each turn, a player should play out every one of the accompanying activities all together. Pick a beginning cell (r1,c1) with non-zero worth. Pick a completing cell (r2,c2) to such an extent that r1≤r2 and c1≤c2. Lessening the worth of the beginning cell by some sure non-zero integer. Pick any of the most limited ways between the two cells and either increment, lessening or leave the upsides of cells on this way unaltered. Note that: a most limited way is one that goes through the most un-number of cells; all cells on this way barring the beginning cell, yet the completing cell might be altered; the subsequent worth of every cell should be a non-negative integer; the cells are changed freely and not really by a similar worth. On the off chance that the beginning and finishing cells are something very…
- Size of sample space A six-sided dice is rolled, a five-sided dice is rolled and a three-sided dice is rolled. Considering this as a probability experiment, what is the size of the sample space? An Event In the context of the probability experiment just described (a 6-sided, a 5-sided, and a 3-sided dice thrown): Consider the event in which two face- up numbers on the three dice add to 10. What is the size of this set? Save ResetFor (∃ x)(P(x,b)) Would an example of this being true if the domain was all the Avengers and x was green skin, then "b" being the Hulk would make this true. Am example of this being false would be: If the domain was all integers and x was positive, even integers and "b" was integers greater than zero.Correct answer will be upvoted else Multiple Downvoted. Don't submit random answer. Computer science. Two cells are adjoining in the event that they share a side. Thusly, every cell (x, y) has precisely three neighbors: (x+1, y) (x−1, y) (x+1, y−1) in case x is even and (x−1, y+1) in any case. At first a few cells are contaminated, all the others are sound. The course of recuperation starts. Each second, for precisely one cell (despite the fact that there may be different cells that could change its state) one of the accompanying occurs: A sound cell with something like 2 contaminated neighbors likewise becomes tainted. A contaminated cell with something like 2 solid neighbors likewise becomes sound. In the event that no such cell exists, the course of recuperation stops. Patient is considered recuperated if the course of recuperation has halted and every one of the cells are solid. We're keen on a most dire outcome imaginable: is it conceivable that the patient…