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Chapter 5: Q 27. (page 297)

Color-blind men Refer to Exercise 25. Suppose we randomly select 4 U.S. adult males. What鈥檚 the probability that at least one of them is red-green

color-blind? Design and carry out a simulation to answer this question. Follow the four-step process.

Short Answer

Expert verified

The outcome will be either 0 or 1 person who is colorblind to red and green.

Step by step solution

01

Step 1. Given Information    

The percentage of men in the United States who suffer from red-green color blindness is 0.07n=4 adults from the United States were randomly selected. Using the four-step design and simulation method, we must determine the likelihood that at least one of them is red-green colorblind.

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   

We'll use two-digit numbers to obtain the answer. Allow the numerals 00to 06to symbolize a person who is colorblind in the red-green spectrum. Allow the numbers 07to 99to represent a person who is not colorblind to red and green. Make a set of four two-digit numbers. Count the number of people who are colorblind in the red-green spectrum. You'll most likely get a result of 0 or 1 person who is colorblind to red and green.

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Most popular questions from this chapter

Sampling senators The two-way table below describes the members of the U.S Senate in a recent year. Male Female Democrats 4713 Republicans 364

(a) Who are the individuals? What variables are being measured?

(b) If we select a U.S. senator at random, what鈥檚 the probability that we choose

  • a Democrat?
  • a female?
  • a female Democrat?
  • a female or a Democrat?

You read in a book about bridge that the probability that each of the four players is dealt exactly one ace is about 0.11 This means that (a) in every100 bridge deals, each player has one ace exactly 11 times.

(b) in one million bridge deals, the number of deals on which each player has one ace will be exactly 110,000

(c) in a very large number of bridge deals, the percent of deals on which each player has one ace will be very close to 11%

(d) in a very large number of bridge deals, the average number of aces in a hand will be very close to 0.11

(e) None of these

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.

Simulation blunders Explain what鈥檚 wrong with each of the following simulation designs.

(a) A roulette wheel has 38colored slots鈥�38 red, 18 black, and 2green. To simulate one spin of the wheel, let numbers 00 to 18 represent red, 19 to 37

represent black, and 38 to 40 represent green.

(b) About 10% of U.S. adults are left-handed. To simulate randomly selecting one adult at a time until you find a left-hander, use two digits. Let 01 to 10 represent being left-handed and 11 to 00 represent being right-handed. Move across a row in Table D, two digits at a time, skipping any numbers that have already appeared, until you find a number between 01 and 10. Record the number of people selected.

An unenlightened gambler

(a) A gambler knows that red and black are equally likely to occur on each spin of a roulette wheel. He observes five consecutive reds occur and bets

heavily on black at the next spin. Asked why he explains that black is 鈥渄ue by the law of averages.鈥� Explain to the gambler what is wrong with this reasoning.

(b) After hearing you explain why red and black are still equally likely after five reds on the roulette wheel, the gambler moves to a poker game. He is dealt five straight red cards. He remembers what you said and assumes that the next card dealt in the same hand is equally likely to be red or black. Is the gambler right or wrong, and why?
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