Scrabble Refer to Exercise 20. About 3% of the time, the first player in Scrabble can “bingo” 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

Teachers and college degrees Select an adult at random. Define events A: a person has earned a college degree, and T: person’s career is teaching. Rank the following probabilities from smallest to largest. Justify your answer.

P(A)P(T)P(A|T)P(T|A)

Liar, liar! Sometimes police use a lie detector (also known as a polygraph) to help determine whether a suspect is telling the truth. A lie detector test isn’t foolproof—sometimes it suggests that a person is lying when they’re actually telling the truth (a “false positive”). Other times, the test says that the suspect is being truthful when the person is actually lying (a “false negative”). For one brand of polygraph machine, the probability of a false positive is 0.08.
(a) Interpret this probability as a long-run relative frequency.
(b) Which is a more serious error in this case: a false positive or a false negative? Justify your answer.

Urban voters The voters in a large city are 40%white, 40%black, and 20%Hispanic. (Hispanics may be of any race in official statistics, but here we are speaking of political blocks.) A mayoral candidate anticipates attracting 30%of the white vote, 90%of the black vote, and 50%of the Hispanic vote. Draw a tree diagram to represent this situation. What percent of the overall vote does the candidate expect to get? Use the four-step process to guide your work.

Lotto In the United Kingdom’s Lotto game, a player picks six numbers from 1 to 49 for each ticket. Rosemary bought one ticket for herself and one for each of her four adult children. She had the lottery computer randomly select the six numbers on each ticket. When the six winning numbers were drawn, Rosemary was surprised to find that none of these numbers appeared on any of the five Lotto tickets she had bought. Should she be? Design and carry

out a simulation to answer this question. Follow the four-step process.

Sampling senators Refer to Exercise 67. Are events D and F independent? Justify your answer.

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