stats chapter 5

In a certain town, 60% of the households have fiber optic internet access, 30% have at least one high-definition television, and 20% have both. The proportion of households that have neither fiber optic internet or high-definition television is:

30%

Students at University Xmust have one of four class ranks-freshman, sophomore, junior, or senior. At University X, 35% of the students are freshmen and 30% are sophomores. If a University X student is selected at random, the probability that he or she is either a junior or a senior is

35%

Event A occurs with probability .3, and event B occurs with probability .4. If A and B age independent, we may conclude that

P(A and B)=.12 P(A|B)=.3 P(B|A)=.4 all of the above

I select two cards from a deck of 52 cards and observe the color of each (26 cards in the deck are red and 26 are black). Which of the following is an appropriate sample space S for the possible outcomes?

S= { (red, red) , (red, black), (black, red), (black, black)}, where, for example, (red, red) stands for the event "the first card is red and the second card is red."

Ignoring twins and other multiple births, assume that babies born at a hospital are independent random events with the probability that a baby is a boy and the probability that a baby is a girl both equal to 0.5. The probability that the next five babies are girls is

.03125

suppose that A and B are independent events with P(A)=.2 and P(B)=.4 P(AvB) is:

.12

Event A has probability 0.4. Event B has probability 0.5. If A and B are independent, then the probability that both events occur is

.2

A ten-sided die has each of the digits from 0 to 9 on one of its faces. Which of the following best describes what it means to say that the probability of rolling a 3 is 0.1?

If you roll the die thousands of times, the proportion of times that you roll a 3 will be close to 0.1

if the knowledge that an event A has occurred implies that a second event B cannot occur, the events A and B are said to be

disjoint

If I toss a fair coin 5000 times

the proportion of heads with be close to 0.5

here is an assignment of probabilities to the face that comes up when rolling an unusual die once: 1. 1/7 2. 2/7 3. 0 4. 4/7 5. 0 6. 1/7 which of the following is true?

this isnt a legitimate assignment of probability

the probability that the student takes neither chemistry nor Spanish is

.4

Event A occurs with a probability 0.8. The conditional probability that event B occurs, given that A occurs, is .5. The probabilitythat both A and B occur is

.4

if you draw an m&m candy at random from a bag of the candies, the candy you draw will have one of six colors. The probability of drawing each color depends on the proportion of each color among all candies made. The table below gives the probability that a randomly chosen M&M had each color before blue M&M's replaced tan in 1995. brown .3 red .2 yellow ? green .1 orange .1 tan .1 the probability that you draw either a brown or a green candy is

.4

A student is chosen at random from the River City High school student body, and the following events are recorded M = the student is male F = The student is female B = The student ate breakfast that morning N = The student did not eat breakfast that morning The following tree diagram gives probabilities associated eith these events. B .8/ M< .4/ .2\ / N \ B .6\ .3 / F< .7 \ N What is the probability that the student had breakfast?

.5

The following table compares the hand dominance of 200 Canadian high-school students and what methods they prefer to communicate with their friends cell phone/ person. online. total text. left. 12. 13 9. 34 right. 43. 72. 51. 166 total. 55. 85. 60. 200 suppose one student is chosen randomly from this group if 200 What is the probability that the student chosen is left handed or prefers to communicate with friends in person

.53

you ask a sample of 379 people, "should clinical trials on issues such add heart attacks that affect both sexes use subject ood just one sex?" The responses are in the table below yes. male. Male. 34 105 female 46. 185 what is the probability that the person is a woman, given that she said yes?

.575

the Venn diagram below describes the proportion of students who take chemistry and Spanish at Jefferson High School, where A= student takes chemistry and B= student takes Spanish suppose one student is chose at random. A B .2○.1○.3 Find the valve of P(AUB) and describe our in words.

.6 the probability that the student takes either chemistry or Spanish or both

One hundred high school students were asked if they had a dog a cat, or both at home. Here are the results. dog? total no. yes. cat.? no. 74. 4. 78 yes. 10. 12. 22 total. 84. 16. 100 If two students are selected at random, what is the probability that neither of them has a dog or a cat?

.548

The card game Euchre uses a deck whith 32 cards: ace, king, queen, Jack, 10, 9, 8, 7 of each suit. Suppose you choose one card at random from a well-shuffled Euchre deck. What is the probability that the card is a Jack, given that you know it is a face card

1/3

the collection of all possible outcomes of a random phenomenon is called

the sample space

if you draw an m&m candy at random from a bag of the candies, the candy you draw will have one of six colors. The probability of drawing each color depends on the proportion of each color among all candies made. The table below gives the probability that a randomly chosen M&M had each color before blue M&M's replaced tan in 1995. brown .3 red .2 yellow ? green .1 orange .1 tan .1 the probability of drawing a yellow candy is

.2

you ask a sample of 379 people, "should clinical trials on issues such add heart attacks that affect both sexes use subject ood just one sex?" The responses are in the table below yes. male. Male. 34 105 female 46. 185 What is the probability that the person said yes, given she is a woman?

.2

A student is chosen at random from the River City High school student body, and the following events are recorded M = the student is male F = The student is female B = The student ate breakfast that morning N = The student did not eat breakfast that morning The following tree diagram gives probabilities associated eith these events. B .8/ M< .4/ .2\ / N \ B .6\ .3 / F< .7 \ N find the P(B|F)and write in words what this expression represents.

.30 thw probability the student ate breakfast given she is female.

if you draw an m&m candy at random from a bag of the candies, the candy you draw will have one of six colors. The probability of drawing each color depends on the proportion of each color among all candies made. The table below gives the probability that a randomly chosen M&M had each color before blue M&M's replaced tan in 1995. brown .3 red .2 yellow ? green .1 orange .1 tan .1 the probability that you do not draw a red candy is

.8

Ignoring twins and other multiple births, assume that babies born at a hospital are independent random events with the probability that a baby is a boy and the probability that a baby is a girl both equal to 0.5. the probability that at least one of the next three babies is a boy is

.875

Event A has probability 0.4. Event B has probability 0.5. If A and B are disjoint, then the probability that both events occur is

0

A basketball player makes 160 out of 200 free throws. we would estimate the probability that the player makes his next free throw to be

0.80.

I toss a penny and observe whether it lands heads up or tails up. Suppose the penny is fair, i.e., the probability of heads is 1/2 and the probability of tails is 1/2. This means that

if I flip the coin many, many times the proportion of heads will be approximately 1/2,and this proportion will tend to get closer and closer to 1/2 as the number of tosses increase.

A plumbing contractor puts in bids on two large jobs. let A=the event that the contractor wins the first contact and let B= the event that the contractor win vs. the second contract. Which of the following Venn diagrams had correctly shaded the event that the contractor wins exactly one of the contracts?

iyer is the one with both of A and B shaded and nothing else

The letters p, q, r, and s represent probabilities for the four distinct regions in the Venn diagram below. For each question, indicate which expression describes the probability of the event indicated. A B q○r○s p P(AUB)

q+s+r

The letters p, q, r, and s represent probabilities for the four distinct regions in the Venn diagram below. For each question, indicate which expression describes the probability of the event indicated. A B q○r○s p the probability associated with the intersection of A and B.

r

A student is chosen at random from the River City High school student body, and the following events are recorded M = the student is male F = The student is female B = The student ate breakfast that morning N = The student did not eat breakfast that morning The following tree diagram gives probabilities associated eith these events. B .8/ M< .4/ .2\ / N \ B .6\ .3 / F< .7 \ N What is the probability that the selected student is male and ate breakfast?

.32

The following table compares the hand dominance of 200 Canadian high-school students and what methods they prefer to communicate with their friends cell phone/ person. online. total text. left. 12. 13 9. 34 right. 43. 72. 51. 166 total. 55. 85. 60. 200 suppose one student is chosen randomly from this group if 200 if you know the person that has been randomly selected is left handed, what is the probability that they prefer to communicate with friends in person?

.382

A student is chosen at random from the River City High school student body, and the following events are recorded M = the student is male F = The student is female B = The student ate breakfast that morning N = The student did not eat breakfast that morning The following tree diagram gives probabilities associated eith these events. B .8/ M< .4/ .2\ / N \ B .6\ .3 / F< .7 \ N Given that a student eco age breakfast is selected, what is the probability that he is male?

.64

One hundred high school students were asked if they had a dog a cat, or both at home. Here are the results. dog? total no. yes. cat.? no. 74. 4. 78 yes. 10. 12. 22 total. 84. 16. 100 If a single student is selected at random and you know she has a dog, what is the probability she also has a cat?

.75

A poker player is dealt poor hands for several hours. He decides to bet heavily on the last hand of the evening on the grounds that after many bad hands he is due for a winner.

He's wrong, because successive deals are independentof each other.

An assignment of probabilities must obey which of the following?

The probability of any event must be a number hetween 0 and 1, inclusive. The sum of all the probabilities of all outcomes in the sample space must be exactly 1. The probability of an event is the sum of the probabilities of outcomes in the sample space in which the event occurs. All three of the above.

You are playing a board game with some friends that involves rolling two six-sided dice. For eight consecutive rolls, the sum on the dice is 6. Which of the following statements is true?

The probability of rolling a 6 on the ninth roll is the same as it was on the first roll.

Ignoring twins and other multiple births, assume that babies born at a hospital are independent random events with the probability that a baby is a boy and the probability that a baby is a girl both equal to 0.5. the events A= the next two babies are boys, and B= the next two babies are girls are

disjoint

In probability and statistics, a random phenomenon is

something that is unpredictable from one occurrence to the next, but over the course of many occurrences follows a predictable pattern.