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- Five people (Alex, Byron, Chloe, Dexter, and Emily) form a club, N = {A, B, C, D, E). Chloe and Emily are women, and the others are men. If they choose a president randomly, find the odds against Emily becoming president. The odds against Emily becoming president are to (Type whole numbers.)In a typical package of jellybeans, 40% of the candies are orange. Five, 5, jellybeans are selected from small jellybean package that contains 20 candies. If X represents the number of orange jellybeans, then determine each of the following. Show all work, use proper notation and provide a therefore statement. Round to the nearest thousandth (3 decimal places) for each probability. a) P(X = 3) if each jellybean is put back in the package after it is selected. b) P(X = 3) if each jellybean is not put back in the bag after it is selected. c) E(X) if each jellybean is put back in the bag after it is selected.Students take a test twice and a researcher wants to know if the firest try is a higher score that the second try at the .05 level. Student 1 Student 2 Student 3 Student 4 Student 5 Student 6 Student 7 Student 8 33 35 28 29 32 32 30 34 27 29 32 31 30 29 28 22 (Put: L-Left Tailed, R- Right Tailed, 2 - 2-Tailed) (separate with a comma if there are 2) Try 1 Try 2 1. The graph is 2. The critical value is 3. The test statistic is 4. The 3-decimal p-value is 5. The test statistice is where compared to the CV? (the letter L - Left, M - Middle, R-Right)
- In the spreading of a rumour, each person who is told the rumour has probability p of believing it and only those who believe the rumour will pass it on. Assume that all individuals behave independently of each other and the rumour is never told to someone who has already heard it. Assume also that each person who is told the rumour and believes it on the n-th day will pass the rumour on to two other people on the (n + 1)-st day. Suppose that the rumour originates on day 1 from a single individual telling the rumour to two other people. Let Zo = 1 and for n ≥ 1 denote by Z₁, the number of people who are told the rumour on day n and believe it. (i) Explain why (Zn)nzo is a branching process. (ii) Find the probability mass function and the probability generating function of Z₁. (iii) What is the probability that the spread of the rumour ultimately ceases? (iv) For what values of p is the spread of the rumour certain to cease eventually? (v) For n ≥ 1 show that P(Zn = 2") = p2¹ +22+ +2″Q2) 10 cards numbered 1-10 are Shuffled. The top and bottom card are chosen. S: Sum of the two cards. Find the probability distribuhon of S, E(S), E (S²) and Var (x)When one die is rolled, the following six outcomes are possible. Six dice are shown, ranging from 1 dot to 6 dots each in increments of 1. List the outcomes constituting A = event the die comes up even, B = event the die comes up 3 or more, C = event the die comes up at most 3, D = event the die comes up 6. What outcomes constitute event A? 3636 (Use a comma to separate answers as needed. Use ascending order.)
- Zia drew 10 cards in order from an ordinary deck of cards, returning the card each time and if the number of red cards drawn is at most 2, she will give her mother a 5,000 worth SM gift certificate. Otherwise, she will buy her new kitchenware. Which of the following statement(s) is(are) TRUE? * O Let X bethe number of red cards drawn. Then X binomial(10,0.5) The probability that she will buy her mother a new kitchenware is 0.0547 O Both I and II O Neither I nor II Suppose it has been observed that an average of 180 vehicles passes by 1 their house between 8 and 9 AM on Wednesday mornings. During that time slot on any Wednesday morning, Zia counted the number of passing vehicles. If at most 3 vehicles pass by their house in any two minutes, she will give her mother a new watch. Otherwise, she will give her a necklace. Which of the following statement(s) is(are) TRUE? * The number of vehicles passing by Zia's house in two minutes deviates from the mear of 180 by 180. O The probability…The TAs invite some other friends to join in on their Barbie watch party. Among the 2 ≤ k ≤ 7people at the watch party, what is the probability that at least two of them were born on thesame day of the week?From the help of the attached image, show every formula used for each step in excel.
- the numbers 1 to 30 are written on cards. If one card is chosen at random, what is the probability that the number on the card will be? a. a factor of 36? b. one with 4 as a digit? c. greater than 12?solve d of 4Using the pigeonhole principle Assuming no one has more than 1,000,000 hairs on the head of any person and that the population of Manila was 11,621,500 in 2009, there had to be at least _____ people in Manila in 2009 with the same number of hairs on their heads.