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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

Two fair dice are tossed, and the face on each die is observed.

  1. Use a tree diagram to find the 36 sample points contained in the sample space.
  2. Assign probabilities to the sample points in part a.
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(2) H H T T H T T H HH

(3) T TTTTTTTTT

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  2. Find the probability that the 10 coin tosses result in all heads or all tails.
  3. Find the probability that the 10 coin tosses result in a mix of heads and tails.
  4. Marilyn鈥檚 answer to the question posed was 鈥淭hough the chances of the three specific sequences occurring randomly are equal . . . it鈥檚 reasonable for us to choose sequence (2) as the most likely genuine result.鈥� If you know that only one of the three sequences actually occurred, explain why Marilyn鈥檚 answer is correct. [Hint: Compare the probabilities in parts b and c.]

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Three fair coins are tossed and either heads(H) or tails(T) are observed for each coin.

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