Section 5.1 HW

A baseball player hit 60 home runs in a season. Of the 60 home​ runs, 24 went to right​ field, 16 went to right center​ field, 9 went to center​ field, 10 went to left center​ field, and 1 went to left field. ​(Round to three decimal places as​ needed.) ​(a) What is the probability that a randomly selected home run was hit to right​ field? ​(b) What is the probability that a randomly selected home run was hit to left​ field? ​(c) Was it unusual for this player to hit a home run to left​ field? Explain. ​(c) Was it unusual for this player to hit a home run to left​ field? A. ​No, because the probability of an unusual event is 0. B. ​Yes, because​ P(left ​field)<0.5. C. ​Yes, because​ P(left ​field)<0.05. D. ​No, because this player hit 1 home runs to left field.

a. 0.352 b. 0.014 c. ​Yes, because​ P(left ​field)<0.05.

True or False​: In a probability​ model, the sum of the probabilities of all outcomes must equal 1.

true

True or False​: Probability is a measure of the likelihood of a random phenomenon or chance behavior.

true

Which of the following numbers could be the probability of an​ event? 0, 1.43, 0.01, 1, 0.22, -0.47 The numbers that could be a probability of an event are ________. ​(Use a comma to separate answers as​ needed.)

0, 0.01, 0.22, 1

Let the sample space be S={1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Suppose the outcomes are equally likely. Compute the probability of the event E={2, 3, 6}. P(E) = _______ ​(Type an integer or a decimal. Do not​round.)

0.3

Let the sample space be S={1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.Suppose the outcomes are equally likely. Compute the probability of the event E=​"an even number less than 9​." P(E) = __________ ​(Type an integer or a decimal. Do not​ round.)

0.4

According to a certain​ country's department of​ education, 43.8​% of​ 3-year-olds are enrolled in daycare. What is the probability that a randomly selected​ 3-year-old is enrolled in day​ care? The probability that a randomly selected​ 3-year-old is enrolled in day care is __________. ​(Type an integer or a​ decimal.)

0.438

What does it mean for an event to be​ unusual? Why should the cutoff for identifying unusual events not always be​ 0.05? A. An event is unusual if it has a probability equal to 0. The choice of a cutoff should consider the context of the problem. B. An event is unusual if it has a probability equal to 1. The choice of a cutoff should consider the context of the problem. C. An event is unusual if it has a low probability of occurring. The choice of a cutoff should consider the context of the problem. D. An event is unusual if it has a high probability of occurring. The choice of the cutoff should consider the context of the problem.

An event is unusual if it has a low probability of occurring. The choice of a cutoff should consider the context of the problem.

Describe the difference between classical and empirical probability. A. The empirical method obtains an exact empirical probability of an event by conducting a probability experiment. The classical method of computing probabilities does not require that a probability experiment actually be performed.​ Rather, it relies on counting​ techniques, and requires equally likely outcomes. B. The classical method obtains an approximate empirical probability of an event by conducting a probability experiment. The empirical method of computing probabilities does not require that a probability experiment actually be performed.​ Rather, it relies on counting​ techniques, and requires equally likely outcomes. C. The empirical method obtains an approximate empirical probability of an event by conducting a probability experiment. The classical method of computing probabilities does not require that a probability experiment actually be performed.​ Rather, it relies on counting​ techniques, and requires equally likely outcomes. D. The classical method obtains an exact probability of an event by conducting a probability experiment. The empirical method of computing empirical probabilities does not require that a probability experiment actually be performed.​ Rather, it relies on counting​ techniques, and requires equally likely outcomes.

The empirical method obtains an approximate empirical probability of an event by conducting a probability experiment. The classical method of computing probabilities does not require that a probability experiment actually be performed.​ Rather, it relies on counting​ techniques, and requires equally likely outcomes.

Bob is asked to construct a probability model for rolling a pair of fair dice. He lists the outcomes as​ 2, 3,​ 4, 5,​ 6, 7,​ 8, 9,​ 10, 11, 12. Because there are 11​ outcomes, he​ reasoned, the probability of rolling a five must be 1/11. What is wrong with​ Bob's reasoning? A. The probability of an event is greater than 1. B. The sum of the probabilities of all outcomes does not equal 1. C. The probability of an event is less than 0. D. The experiment does not have equally likely outcomes.

The experiment does not have equally likely outcomes.

In a certain card​ game, the probability that a player is dealt a particular hand is 0.33. Explain what this probability means. If you play this card game 100​ times, will you be dealt this hand exactly 33 ​times? Why or why​ not? A. The probability 0.33 means that approximately 33 out of every 100 dealt hands will be that particular hand.​ No, you will not be dealt this hand exactly 33 times since the probability refers to what is expected in the​ long-term, not​ short-term. B. The probability 0.33 means that exactly 33 out of every 100 dealt hands will be that particular hand.​ Yes, you will be dealt this hand exactly 33 times since the probability refers to​ long-term behavior, not​ short-term. C. The probability 0.33 means that exactly 33 out of every 100 dealt hands will be that particular hand.​ Yes, you will be dealt this hand exactly 33 times since the probability refers to​ short-term behavior, not​ long-term. D. The probability 0.33 means that approximately 33 out of every 100 dealt hands will be that particular hand.​ No, you will not be dealt this hand exactly 33 times since the probability refers to what is expected in the​ short-term, not​ long-term.

The probability 0.33 means that approximately 33 out of every 100 dealt hands will be that particular hand.​ No, you will not be dealt this hand exactly 33 times since the probability refers to what is expected in the​ long-term, not​ short-term.

A bag of 100 tulip bulbs purchased from a nursery contains 30 red tulip​ bulbs, 25 yellow tulip​ bulbs, and 45 purple tulip bulbs. ​(Type an integer or a decimal. Do not​ round.) ​(a) What is the probability that a randomly selected tulip bulb is​ red? ​(b) What is the probability that a randomly selected tulip bulb is​ purple? ​(c) Interpret these two probabilities. A. If 100 tulip bulbs were sampled with​ replacement, one would expect exactly ______ of the bulbs to be red and exactly ______ of the bulbs to be purple. B. If 100 tulip bulbs were sampled with​ replacement, one would expect about ______ of the bulbs to be red and about ______ of the bulbs to be purple.

a 0.3 b 0.45 c If 100 tulip bulbs were sampled with​ replacement, one would expect about 30 of the bulbs to be red and about 45 of the bulbs to be purple.

​(Type an integer or a​ decimal.) a. What is the probability of an event that is​ impossible? b. Suppose that a probability is approximated to be zero based on empirical results. Does this mean that the event is​ impossible?

a. 0 b. No

The table shows the results of rolling a fair​ six-sided die. Complete parts ​(a) through ​(d) below. ​(Round to two decimal places as​ needed.) Outcome on Die 100 Trials 100 Trials 500 Trials 1 19 20 79 2 18 15 87 3 15 13 81 4 21 15 77 5 14 15 88 6 13 22 88 (a) Using the​ table, find the empirical probability of rolling a 3 for the first 100 trials. The empirical probability of rolling a 3 for the first 100 trials is ______. ​(b) Using the​ table, find the empirical probability of rolling a 3 for the second 100 trials. The empirical probability of rolling a 3 for second 100 trials is ________. (c) Using the​ table, find the empirical probability of rolling a 3 for 500 trials. The empirical probability of rolling a 3 for 500 trials is ______. ​(d) Compare the empirical probabilities to the probability obtained using the classical​ method, and explain what they show. A. All the empirical probabilities are equal to the classical probability. This is an outcome expected according to the Law of Large Numbers. B. The empirical probabilities approach the classical probability as the sample size increases. This is an outcome expected according to the Law of Large Numbers. C. The empirical probabilities are all equally far away from the classical probability. This is an outcome expected according to the Law of Large Numbers. D. The empirical probability is closest to the classical probability for the two sets of 100 trials and gets farther away for the 500 trials. This is an outcome expected according to the Law of Large Numbers.

a. 0.15 b. 0.13 c. 0.16 d. The empirical probabilities approach the classical probability as the sample size increases. This is an outcome expected according to the Law of Large Numbers.

A survey of 200 randomly selected high school students determined that 184 play organized sports. ​(Round to the nearest thousandth as​ needed.) ​(a) What is the probability that a randomly selected high school student plays organized​ sports? ​(b) Interpret this probability. A. If​ 1,000 high school students were​ sampled, it would be expected that exactly ______ of them play organized sports. B. If​ 1,000 high school students were​ sampled, it would be expected that about ______ of them play organized sports.

a. 0.92 b. If​ 1,000 high school students were​ sampled, it would be expected that about 920 of them play organized sports.

Determine whether the probabilities below are computed using the classical​ method, empirical​ method, or subjective method. Complete parts ​(a) through ​(d) below. ​(a) The probability of having eight girls in an eight​-child family is 0.00390625. A. Empirical method B. Subjective method C. Classical method D. It is impossible to determine which method is used. ​(b) On the basis of a survey of 1000 families with eight ​children, the probability of a family having eight girls is 0.0065. A. Empirical method B. Subjective method C. Classical method D. It is impossible to determine which method is used. (c) According to a sports​ analyst, the probability that a football team will win the next game is 0.35. A. Classical method B. Subjective method C. Empirical method D. It is impossible to determine which method is used. ​(d) On the basis of clinical​ trials, the probability of efficacy of a new drug is 0.82. A. Classical method B. Empirical method C. Subjective method D. It is impossible to determine which method is used.

a. Classical method b. Empirical method c. Subjective method d. Empirical method

Is the following a probability​ model? What do we call the outcome ​"red​"? color experiment red 0 green 0.1 blue 0.25 brown 0.3 yellow 0.1 orange 0.2 a. Is the table above an example of a probability​ model? A. No​, because the probabilities do not sum to 1 . B.Yes, because the probabilities sum to 1. C. ​No, because not all the probabilities are greater than 0. D. Yes, because the probabilities sum to 1 and they are all greater than or equal to 0 and less than or equal to 1. b. What do we call the outcome ​"red​"? A. Certain event B. Impossible event C. Unusual event D. Not so unusual event

a. No​, because the probabilities do not sum to 1 . b. impossible event

In a national survey college students were​ asked, "How often do you wear a seat belt when riding in a car driven by someone​ else?" The response frequencies appear in the table to the right.​ (a) Construct a probability model for​ seat-belt use by a passenger.​ (b) Would you consider it unusual to find a college student who never wears a seat belt when riding in a car driven by someone​ else? ​(Round to the nearest thousandth as​ needed.) Response Frequency Never 117 Rarely 344 Sometimes 535 Most of the time 1384 Always 2274 ​(a) Complete the table below. Response Probability Never ______ Rarely _____ Sometimes _____ Most of the time _____ Always _____ (b) ​(b) Would you consider it unusual to find a college student who never wears a seat belt when riding in a car driven by someone​ else? A. ​No, because the probability of an unusual event is 0. B. ​No, because there were 117 people in the survey who said they never wear their seat belt. C. ​Yes, because 0.01<​P(never)<0.10. D. ​Yes, because ​P(never)<0.05.

a. Response Probability Never 0.025 Rarely 0.074 Sometimes 0.115 Most of the time 0.297 Always 0.489 b. ​Yes, because ​P(never)<0.05.

In a certain game of​ chance, a wheel consists of 44 slots numbered​ 00, 0,​ 1, 2,..., 42. To play the​ game, a metal ball is spun around the wheel and is allowed to fall into one of the numbered slots. Complete parts​ (a) through​ (c) below. ​(a) Determine the sample space. Choose the correct answer below. A. The sample space is​ {00, 0}. B. The sample space is​ {00, 0,​ 1, 2,..., 42​}. C. The sample space is​ {1, 2,..., 42​}. D. The sample space is​ {00}. ​(b1) Determine the probability that the metal ball falls into the slot marked 6. Interpret this probability. The probability that the metal ball falls into the slot marked 6 is _______. ​(Round to four decimal places as​ needed.) (b2) Interpret this probability. Select the correct choice below and fill in the answer box within your choice. ​(Type a whole​ number.) A. If the wheel is spun 1000​ times, it is expected that exactly ______ of those times result in the ball not landing in slot 6. B. If the wheel is spun 1000​ times, it is expected that about ______ of those times result in the ball landing in slot 6. (c1) Determine the probability that the metal ball lands in an odd slot. Interpret this probability. The probability that the metal ball lands in an odd slot is _____. ​(Round to four decimal places as​ needed.) (c2) Interpret this probability. Select the correct choice below and fill in the answer box within your choice. ​(Type a whole​ number.) A. If the wheel is spun 100​ times, it is expected that exactly ________ of those times result in the ball not landing on an odd number. B. If the wheel is spun 100​ times, it is expected that about ________ of those times result in the ball landing on an odd number.

a. The sample space is​ {00, 0,​ 1, 2,..., 42​}. b1. 0.0227 b2. If the wheel is spun 1000​ times, it is expected that about 23 of those times result in the ball landing in slot 6. c1. 0.4773 c2. 48

​A(n) _____________ is any collection of outcomes from a probability experiment.

event

In​ probability, a(n)​ ________ is any process that can be repeated in which the results are uncertain.

experiment