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Chapter 3: Q22E (page 171)

Jai-alai bets. The Quinella bet at the paramutual game of jai-alai consists of picking the jai-alai players that will place first and second in a game irrespective of order. In jai-alai, eight players (numbered 1, 2, 3, . . . , 8) compete in every game.

a. How many different Quinella bets are possible?

b. Suppose you bet the Quinella combination of 2鈥�7. If the players are of equal ability, what is the probability that you win the bet?

Short Answer

Expert verified
  1. 28
  2. 45/7

Step by step solution

01

Step-by-Step SolutionStep 1: Identify the different possible Quinella bets

The possibility of an event occurring is defined by probability. We may be required to forecast the result of an event in various real-life situations. To us, the result of an event might be certain or unknown.

Here, we have 8 players in the game, and we are selecting a person who has placed first and second in this game.

Therefore, we were only interested in two players and did not consider an order.

Probability=C28=8!2!脳(8-2)!=8脳7脳6脳5脳4脳3脳2脳12脳1脳6脳5脳4脳3脳2脳1=28

Hence, the different possible Quinella bets are 28.

02

Identify the probability of winning the bet

The possibility that wins the bet is:

P(winthebet)=No.ofpossibleoutcomesTotaloutcomes=C2628=6!2!脳2!28=6脳5脳4脳3脳2脳12脳1脳2脳128=18028=457

Hence, the probability of winning the bet is45/7.

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Most popular questions from this chapter

Confidence of feedback information for improving quality. In the semiconductor manufacturing industry, a key to improved quality is having confidence in the feedback generated by production equipment. A study of the confidence level of feedback information was published in Engineering Applications of Artificial Intelligence(Vol. 26, 2013). At any point in time during the production process, a report can be generated. The report is classified as either 鈥淥K鈥� or 鈥渘ot OK.鈥� Let Arepresent the event that an 鈥淥K鈥� report is generated in any time period (t).Let Brepresent the event that an 鈥淥K鈥� report is generated in the next time period. Consider the following probabilities:

P(A)=0.8,PBA=0.9, andPBAC=0.5.

a. Express the event B|Ain the words of the problem.

b. Express the event B|ACin the words of the problem.

c. FindP(AC).

d. FindP(A鈭�B).

e. FindP(AC鈭�B).

f. Use the probabilities, parts d and e, to find P(B).

g. Use Bayes鈥� Rule to find P(A|B), i.e., the probability that an 鈥淥K鈥� report was generated in one time period(t), given that an 鈥淥K鈥� report is generated in the next time period(t+1).

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Male nannies. In a survey conducted by the International Nanny Association (INA) and reported on the INA Web site (www.nanny.org), 4,176 nannies were placed in a job in a given year. Only 24 of the nannies placed were men. Find the probability that a randomly selected nanny placed during the last year is a male nanny (a 鈥渕annie鈥�).

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Suppose the events B1and B2are mutually exclusive and complementary events, such thatP(B1)=.75andP(B2)=.25 Consider another event A such that role="math" localid="1658212959871" P(AB1)=.3, role="math" localid="1658213029408" P(AB2)=.5.

  1. FindP(B1鈭�A).
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