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Chapter 5: Q. T5.8 (page 357)
In a class, there are 18 girls and 14 boys. If the teacher selects two students at random to attend a party with the principal, what is the probability that the two students are the same sex?
a.
b.
c.
d.
e.
The probability is
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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 that consecutive reds have occurred and bets heavily on
black at the next spin. Asked why, he explains that “black is due.” Explain to the
gambler what is wrong with this reasoning.
b. After hearing you explain why red and black are still equally likely after reds on the
roulette wheel, the gambler moves to a card game. He is dealt straight red cards from
a standard deck withred cards and black 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.
Explain to the gambler what is wrong with this reasoning.
BMI (2.2, 5.2, 5.3) Your body mass index (BMI) is your weight in kilograms divided by
the square of your height in meters. Online BMI calculators allow you to enter weight in
pounds and height in inches. High BMI is a common but controversial indicator of being
overweight or obese. A study by the National Center for Health Statistics found that the
BMI of American young women (ages 20 to 29) is approximately Normally distributed
with mean 26.8 and standard deviation 7.4.
27
a. People with BMI less than 18.5 are often classed as “underweight.” What percent of
young women are underweight by this criterion?
b. Suppose we select two American young women in this age group at random. Find the
probability that at least one of them is classified as underweight.
Which of the following is a correct way to perform the simulation?
a. Let integers from represent making a free throw and represent missing a free throw. Generate random integers from. Count the number
of made free throws. Repeat this process many times.
b. Let integers from represent making a free throw and represent missing a free throw. Generate 50 random integers from 1 to 50 with no repeats
allowed. Count the number of made free throws. Repeat this process many times.
c. Let integers fromrepresent making a free throw and represent missing a free throw. Generate 50 random integers fromCount the number of made free throws. Repeat this process many times.
d. Let integers from localid="1653986588937" represent making a free throw and localid="1653986593808" represent missing a free throw. Generate 50 random integers from localid="1653986598680" with no repeats allowed. Count the number of made free throws. Repeat this process many times.
e. None of the above is correct.
Is this your card? A standard deck of playing cards (with jokers removed) consists of 52 cards in four suits—clubs, diamonds, hearts, and spades. Each suit has 13 cards, with denominations ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, and king. The jacks, queens, and kings are referred to as “face cards.” Imagine that we shuffle the deck thoroughly and deal one card. The two-way table summarizes the sample space for this chance process based on whether or not the card is a face card and whether or not the card is a heart.
| Type of card | |||
| Face card | Non-Face card | Total | |
| Heart | |||
| Non-Heart | |||
| Total | |||
Are the events “heart” and “face card” independent? Justify your answer.
Lefties A website claims that of U.S. adults are left-handed. A researcher believes that this figure is too low. She decides to test this claim by taking a random sample of U.S. adults and recording how many are left-handed. Four of the adults in the sample are left-handed. Does this result give convincing evidence that the website’s claim is too low? To find out, we want to perform a simulation to estimate the probability of getting or more left-handed people in a random sample of size from a very large population in which of the people are left-handed.
Let to indicate left-handed and to 99 represent right-handed. Move left to Page Number: right across a row in Table . Each pair of digits represents one person. Keep going until you get different pairs of digits. Record how many people in the simulated sample are left-handed. Repeat this process many, many times. Find the proportion of trials in which or more people in the simulated sample were left-handed.
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