Partial Question 1 0.5 / 1 pts Select all that apply: If a fair coin is tossed three times successively, then: The probability that exactly two heads appear in three successive tosses is 1/2. The sample space is S={HHH, HHT, HTH, THH, TTH, THT, HTT, TTT, TH, HH, TT, HT}. The probability of each elementary (simple) event equals 1/9. The sample space is S={HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}. The probability that at least two successive outcomes are the same equals 3/4.Question 3 A restaurant tips 15% of their employees via E-transfer, 45% by Cash and 40% by Cheque. Of those employees tipped by E-transfer, 1% get tipped early. Similarly, among those tipped by Cash, 3% get tipped early, and among those tipped by Cheque, 5% get tipped early. Knowing that a randomly selected employee got tipped early, what is the probability that they were tipped via Cash? 0386 0015 0030 0035 0452 Question 4 Select all that apply: Suppose that events A and B are independent, further suppose that P(A)=O.25 and P(B)=O.35, then: P(AUB)=O.5125 P(AlB):0.0875 P(AlB):0 P(B|A):0.25 Events A and B are also mutually exclusive. Question 5 Consider the following table First, compute an appropriate value for the constant a such that p (:L') is a valid probability distribution for the discrete random variable X. Then, select the correct answer(s). P(X=3) = 0.4 P(X1) : 1 P(X23] = 0.6 Question 6 0 / 1 pts Select all that apply: LetX be a random variable denoting the number of goals scored by Lionel Messi in the FIFA World Cup, which has the following probability distribution: :E 0 1 2 3 p (X : 3:) 0.4 0.25 0.20 0.15 The expected value of the number of goals scored by the player is 1.1 The probability that at most 2 goals are scored is 0.65 The variance ofthe number of goals scored by the player is 2.37 The standard deviation of the number of goals scored by the player is 1.54 The probability of the player scoring at least 1 goal is 0.6 Incorrect Question 7 0/2pts Let X be a random variable denoting the number of re hydrants present in a randomly selected road in Mississauga whose probability distribution is given in the following table: 0.1 0.2 0.3 0.2 0.2 Compute the conditional probability P (X 1). 0.33 0.30 0.43 0.86 0.60 m Question 2 0 / 1 \"*5 An urn contains 10 blue and 5 red balls. Two balls are drawn randomly from the urn, one after the another and without replacement. What is the probability that both the rst and second balls drawn are blue? 3/7 10/15 81/196 9/14 4/9