hearts? What is the probability that a five-card poker hand contains the ace of Q2. (6...

 

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hearts? What is the probability that a five-card poker hand contains the ace of Q2. (6 points) What is the probability that a five-card poker hand contains a straight flush, that is, five cards of the same suit of consecutive kinds (i.e. <1-2-3-4-5, 2-3-4-5-6, 9-10-J-Q-K, 10-J-Q-K-1>? Q3. (6 points) In a super lottery, a player selects 7 numbers out of the first 80 positive integers. What is the probability that a person wins the grand prize by picking 7 numbers that are among the 11 numbers selected at random by a computer? Section 7.2: Q4. (9 points) What is the probability of these events when we randomly select a permutation of (1, 2, 3}? a. (3 points) 1 precedes 3. b. (3 points) 3 precedes 1. c. (3 points) 3 precedes 1 and 3 precedes 2. Q5. (6 points) Suppose that E and F are events such that p(E)=0.8 and p(F) = 0.6. Show that p (EU F) 0.8 and p (EF) 0.4. Q6. (5 points) What is the conditional probability that exactly four heads appear when a fair coin is flipped five times, given that the first flip came up tails? Q7. (12 points) Find each of the following probabilities when n independent Bernoulli trials are carried out with probability of success p. a. (3 points) the probability of no successes b. (3 points) the probability of at least one success c. (3 points) the probability of at most one success d. (3 points) the probability of at least two successes hearts? What is the probability that a five-card poker hand contains the ace of Q2. (6 points) What is the probability that a five-card poker hand contains a straight flush, that is, five cards of the same suit of consecutive kinds (i.e. <1-2-3-4-5, 2-3-4-5-6, 9-10-J-Q-K, 10-J-Q-K-1>? Q3. (6 points) In a super lottery, a player selects 7 numbers out of the first 80 positive integers. What is the probability that a person wins the grand prize by picking 7 numbers that are among the 11 numbers selected at random by a computer? Section 7.2: Q4. (9 points) What is the probability of these events when we randomly select a permutation of (1, 2, 3}? a. (3 points) 1 precedes 3. b. (3 points) 3 precedes 1. c. (3 points) 3 precedes 1 and 3 precedes 2. Q5. (6 points) Suppose that E and F are events such that p(E)=0.8 and p(F) = 0.6. Show that p (EU F) 0.8 and p (EF) 0.4. Q6. (5 points) What is the conditional probability that exactly four heads appear when a fair coin is flipped five times, given that the first flip came up tails? Q7. (12 points) Find each of the following probabilities when n independent Bernoulli trials are carried out with probability of success p. a. (3 points) the probability of no successes b. (3 points) the probability of at least one success c. (3 points) the probability of at most one success d. (3 points) the probability of at least two successes

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Q1 The probability that a fivecard poker hand contains the ace of hearts can be calculated as follows There are 52 cards in a standard deck and only 1 of them is the ace of hearts A fivecard hand is s... View the full answer