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Suppose you’re playing Texas Hold ’Em Poker, and you are dealt a hand with
a Jack of Clubs and a Queen of Hearts. The river of 5 cards hasn’t been dealt
yet, and you’re hoping to get a straight (5 cards with consecutive ranks, such as
10,J,Q,K,A or 8,9,10,J,Q). What is the
that uses both the Jack and Queen in your hand? (This last part is to keep the
problem simple, since it’s possible to get a straight that uses neither card in your hand, such
as A,2,3,4,5, all in the river. Besides, in those cases, ALL players would have a straight, so
that’s not so good for you!)
Guide: Our goal is to calculate:
P(straight using both cards in hand) = # 5-card combinations that get us a straight with the J & Q
# 5-card combinations overall .
(a) We’ll start with the denominator, which can be done with a single
formula from class: How many 5-card combinations are possible for the
river? (Keep in mind what is in your hand. Note that how many opponents you have
and what is in their hands is irrelevant since their cards are unknown to you. If it helps,
you can think of your opponents’ cards as being indistinguishable from the remaining
cards in the deck.)
(b) For each of the four steps, how many different ways can we choose?
(c) How many different 5-card rivers will give us the cards we need to
get a straight using both cards in our hand?
(d) Answer the original question: what is the probability that we get a straight
that uses both the Jack of Clubs and Queen of Hearts in our hand?
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- Two chefs (Mike and Larry) cook at a diner. Mike cooks twice as many dishes as Larry. ZAGAT has noted that Larry cooks “good” 3 out of four dishes, while Mike cooks “good” four out of ten dishes. You want take your out-of-town visitor for a dinner there. What is the probability that your visitor will have good dining experience?arrow_forwardZane is ordering a sundae at a restaurant, and the server tells him that he can have up to five toppings: a cherry, hot fudge, caramel, peanuts, and butterscotch sauce. Since he cannot decide how many of the toppings he wants, he tells the server to surprise him. If the server randomly chooses which toppings to add, what is the probability that Zane gets just caramel and butterscotch sauce? Express your answer as a fraction or a decimal number rounded to four decimal places.arrow_forwardDan's Diner employs three dishwashers. Al washes 40% of the dishes and breaks only 2% of those he handles. Betty and Chuck each wash 30% of the dishes, and Betty breaks only 2% of hers, but Chuck breaks 4% of the dishes he washes. You go to Dan's for supper one night and hear a dish break at the sink. What's the probability that Chuck is on the job? The probability that Chuck is on the job is. (Round to three decimal places as needed.)arrow_forward
- Dan's Diner employs three dishwashers. Al washes 20% of the dishes and breaks only 1% of those he handles. Betty and Chuck each wash 40% of the dishes, and Betty breaks only 1% of hers, but Chuck breaks 3% of the dishes he washes. You go to Dan's for supper one night and hear a dish break at the sink. What's the probability that Chuck is on the job? The probability that Chuck is on the job is (Round to three decimal places as needed.) An Pasarrow_forwardYour friend throws two dice and tells you that one of the dice is a 4. What is the probability that the sum of the dice is 8 or more?arrow_forwardEvan is ordering dessert, and he wants the fudge pie. The waitress tells him that he can have up to four toppings: ice cream, chocolate sauce, whipped cream, and a cherry. Since he cannot decide how many of the toppings he wants, he tells the waitress to surprise him. If the waitress randomly chooses which toppings to add, what is the probability that Evan gets just chocolate sauce, and a cherry.arrow_forward
- Bonnie and Connie are twins with identical purses. Bonnie needs 35 cents to pay for a parking meter. Suppose that Bonnie's purse has 5 quarters, 3 dimes, and 2 nickels while Connie's purse has 2 quarters, 5 dimes, and 3 nickels in it. Not being able to tell the difference between the purses, Connie picks one at random and grabs two coins from it. What is the probability that Bonnie picked her own purse given that she drew out enough change to pay for her parking meter? (Note: Bonnie needs to put in at least 35 cents to pay her parking meter.)arrow_forwardA slot machine has 3 dials. Each dial has 30 positions, one of which is "Jackpot". To win the jackpot, all three dials must be in the "Jackpot" position. Assuming each play spins the dials and stops each independently and randomly, what are the odds of one play winning the jackpot? 1/30 = 0.03 or 3% 3/(30+30+30) = 3/90 = 0.33 or 33% 3/(30×30×30) = 3/27000 = 0.0001 or 0.01% 1/(30×30×30) = 1/27000 = 0.00003 or 0.003% Question 18arrow_forward
- A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON
