1. A coin is flipped four times. Assume all outcomes are equally likely. What is the probability that there are at least two consecutive flips that come up heads? 2. A hand of 5 cards is drawn from a standard deck of 52 cards. Assume all outcomes are equally likely. What is the probability that at least two of the cards have the same rank? Hint: Find the probability of the complement.
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- If the probability of an event is 62%, what is the probability of its complement?Assume that, with probability 0.8, It’s going to snow and/or I’m going to stay at home; and with probability 0.7, when it snows, then I stay at home. What is the probability of being truth that I am going to stay at home?2. Given a Sample Space S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}, Event A = {1, 3, 4, 7, 9}, and Event B = {3, 7, 9, 11, 12, 13} Find the probability P(A|B). State your answer as a value with one digit after the decimal point.
- Solve it and provide the 100% correct answer with covering of all test cases.Using R, Use the Monte Carlo simulation to estimate the probability that all six faces appear exactly once in six tosses of fair dice.Two Dice were tossed. What is the probability that the total of two dice will be greater than 9, given that the first die is a 5? (Show your work)
- Test the validity of the following argument, for this make use of the truth tables. If I study, then I won't fail the agent contest. If I don't play football, then I'll study. But I failed the agent contest. Soon, I must have played football.I have a hand of five cards, n of which are aces. An observation is: I shuffle the cards, pick one at random, and show it to you. You are estimating n by counting the total number of aces (let's denote it k) in m observations, and then computing 5k m You may assume that 1This question involves data from which nothing interesting can be learned about frequent itemsets, because there are no sets of items that are correlated. Suppose the items are numbered 1 to 10, and each basket is constructed by including item i with probability 1/i, each decision being made independently of all other decisions. That is, all the baskets contain item 1, half contain item 2, a third contain item 3, and so on. Assume the number of baskets is sufficiently large that the baskets collectively behave as one would expect statistically. Let the support threshold be 1% of the baskets.(a) Find the frequent itemsets.(b) Prove that in this data there are no interesting association rules, i.e., the interest of every association rule is 0.
- Correct answer will be upvoted else Multiple Downvoted. Don't submit random answer. Computer science. Culinary specialist Monocarp has recently put n dishes into a broiler. He realizes that the I-th dish has its ideal cooking time equivalent to ti minutes. At any certain integer minute T Monocarp can put close to one dish out of the broiler. On the off chance that the I-th dish is put out at some moment T, its undesirable worth is |T−ti| — the outright contrast among T and ti. When the dish is out of the stove, it can't return in. Monocarp should put every one of the dishes out of the stove. What is the base all out unsavory worth Monocarp can acquire? Input The principal line contains a solitary integer q (1≤q≤200) — the number of testcases. Then, at that point, q testcases follow. The principal line of the testcase contains a solitary integer n (1≤n≤200) — the number of dishes in the broiler. The second line of the testcase contains n integers t1,t2,… ,tn…For each of the following pairs of events, A and B, determine whether A and B are dependent or not.Show your calculations and briefly explain.(a) We have a deck of 52 playing cards, from which we draw two cards in turn. Let A denote the eventthat the first card we draw is a King. Let B denote the event that the second card we draw is aQueen.(b) We have one fair die (also called a dice). Each of the six faces come up with equal probabilities 1/6.We throw the dice two times in a row. Let A denote the event that the first throw yields a six. LetB denote the event that the second throw yields a six.(c) We draw a bit-string x of length 4 uniformly at random among all bit-strings of length 4. If thehamming weight of x is even, then we draw a bit-string y of length 6 uniformly at random among allbit-strings of length 6. If the hamming weight of x is odd, then we draw a bit-string y of length 42uniformly at random among all bit-strings of length 42. Let A denote the event that the…A certain cat shelter has devised a novel way of making prospective adopters choose their new pet. To remove pet owners’ biases regarding breed, age, or looks, they are led blindfolded into a room containing all the cats up for adoption and must bring home whichever they pick up. Suppose you are trying to adopt two cats, and the shelter contains a total of N cats in one of only two colors: black or orange. is it still possible to pick up two black cats with probability ½, given that there is an even number of orange cats in the room? If so, how many cats should be in the room? How many black, how many orange?