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Chapter 5: Q 26. (page 297)

Scrabble Refer to Exercise 20. About 3% of the time, the first player in Scrabble can 鈥渂ingo鈥� by playing all 7 tiles on the first turn. How many games

of Scrabble would you expect to have to play, on average, for this to happen? Design and carry out a simulation to answer this question. Follow the four step

process.

Short Answer

Expert verified

The outcome will range from 1 to30

Step by step solution

01

Step 1. Given Information 

For each ticket, a player selects six numbers from 1to 49The winning numbers can be represented by two-digit numbers ranging from 1to 49in the simulation. Assume the numbers selected are 33,09,11,18,16and 45

02

Step 2. Concept Used 

We can't foresee the outcomes of a chance process, yet they have a regular distribution over a large number of repetitions. According to the law of large numbers, the fraction of times a specific event occurs in numerous repetitions approaches a single number. The likelihood of a chance outcome is its long-run relative frequency. A probability is a number between 0 (never happens) and 1 (happens frequently) (always occurs).

03

Step 3. Explanation   

Use two-digit numbers instead of three-digit numbers. The numerals 00to 02should stand for "bingo." No "bingo" should be represented by the numbers to 99Count how many two-digit numbers you'll need till you get "bingo." Rep this simulation as many times as you like. Until you get the first "bingo," you'll most likely get a result of 1 to 30 needed numbers.

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Most popular questions from this chapter

Tossing coins Imagine tossing a fair coin 3 times. (a) What is the sample space for this chance

process? (b) What is the assignment of probabilities to outcomes in this sample space?

Playing 鈥淧ick 4鈥� The Pick 4games in many state lotteries announce a four-digit winning number each day. You can think of the winning number as a four-digit group from a table of random digits. You win (or share) the jackpot if your choice matches the winning number. The winnings are divided among all players who matched the winning number. That suggests a way to get an edge.

(a) The winning number might be, for example, either 2873or 9999. Explain why these two outcomes have exactly the same probability.

(b) If you asked many people whether 2873 or 9999 is more likely to be the randomly chosen winning number, most would favor one of them. Use the information in this section to say which one and to explain why. How might this affect the four-digit number you would choose?

Rolling dice Suppose you roll two fair, six-sided dice鈥攐ne red and one green. Are the events 鈥渟um is 7鈥� and 鈥済reen die shows a 4鈥� independent? Justify

your answer.

Are you feeling stressed? (4.1) A Gallup Poll asked whether people experienced stress 鈥渁 lot of the day yesterday.鈥� Forty percent said they did. Gallup鈥檚 report said, 鈥淩esults are based on telephone interviews with 178,545 national adults,

aged 18 and older, conducted Jan. 2鈥�June30,2009.鈥�4

(a) Identify the population and the sample.

(b) Explain how undercover could lead to bias in this survey.

Airport security The Transportation Security Administration (TSA) is responsible for airport safety. On some flights, TSA officers randomly select passengers for an extra security check prior to boarding. One such flight had 76passengers12in first class and 64 in coach class. Some passengers were surprised when none of the 10passengers chosen for screening were seated in first class. We can use a simulation to see if this result is likely to happen by chance.

(a) State the question of interest using the language of probability.

(b) How would you use random digits to imitate one repetition of the process? What variable would you measure?

(c) Use the line of random digits below to perform one repetition. Copy these digits onto your paper. Mark directly on or above them to show how you determined the outcomes of the chance process.
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