stats unit 5 mcq

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

0.2

Use Scenario 5-9. What is the probability that the person said "Yes," given that she is a woman?

0.20

Use Scenario 5-8. Find P(B|F) and write in words what this expression represents.

0.30; The probability the student ate breakfast, given she is female

Use Scenario 5-8. What is the probability that the selected student is a male and ate breakfast?

0.32

Use Scenario 5-11. 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?

0.382

Use Scenario 5-10. The probability that the student takes neither Chemistry nor Spanish is

0.4

Use Scenario 5-8. What is the probability that the student had breakfast?

0.50

Suppose that A and B are independent events with P(A)=0.2and P(B)=0.4. P(AUB) is

0.52

Use Scenario 5-11. What is the probability that the student chosen is left-handed or prefers to communicate with friends in person?

0.53

Use Scenario 5-9. What is the probability that the person is a woman, given that she said "Yes?"

0.575

Use Scenario 5-8. Given that a student who ate breakfast is selected, what is the probability that he is male?

0.64

Use Scenario 5-10. Find the value of P(AUB) and describe it in words.

0.6; The probability that the student takes either chemistry or Spanish, or both.

Use Scenario 5-13. If a single student is selected at random and you know she has a dog, what is the probability she also has a cat?

0.75

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

Use Scenario 5-3. The probability that at least one of the next three babies is a boy is

0.875

Use Scenario 5-13. If a single student is selected at random, what is the probability associated with the union of the events "has a dog" and "does not have a cat?"

0.9

Use Scenario 5-6. The probability that the system functions properly during one period of operation is closest to

0.994

The card game Euchre uses a deck with 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's a face card?

1/3

Use Scenario 5-5. P(A+B)=

1/3

Use Scenario 5-4. The probability that you win $4 both times is

1/36

Use Scenario 5-4. The probability that you win at least $1 both times is

1/4

Suppose there are three cards in a deck, one marked with a 1, one marked with a 2, and one marked with a 5. You draw two cards at random and without replacement from the deck of three cards. The sample space S = {(1, 2), (1, 5), (2, 5)} consists of these three equally likely outcomes. Let X be the sum of the numbers on the two cards drawn. Which of the following is the correct set of probabilities for X?

X-3,6,7 P(X)-1/3,1/3,1/3

Event A occurs with probability 0.3, and event B occurs with probability 0.4. If A and B are independent, we may conclude that

all of the above

An assignment of probabilities must obey which of the following?

all three of the above

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.

In a certain town, 60% of the households have broadband internet access, 30% have at least one high-definition television, and 20% have both. The proportion of households that have neither broadband internet nor high-definition television is:

30%

Students at University X must have one of four class ranks; freshmen, sophomore, junior, 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%

Use Scenario 5-7. The proportion of adults for which the test would be positive is

0.02097

Use Scenario 5-3. The probability that the next five babies are girls is

0.03125

Use Scenario 5-7. If a randomly selected person is tested and the result is positive, the probability the individual has the disease is

0.047.

Use Scenario 5-2. The probability of drawing a yellow candy is

.2

Use Scenario 5-2. The probability that you draw either a brown or a green candy is

.4

Use Scenario 5-2. The probability that you do not draw a red candy is

.8

Use Scenario 5-13. If two students are selected at random, what is the probability that neither of them has a dog or a cat?

0. 548

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

0.0

Suppose that A and B are independent events with P(A)=0.2and P(B)=0.4. P(A+B^c) is

0.12

Use Scenario 5-1. Based on your simulation, the estimated probability of winning nothing is

2/11

A basketball player makes 75% of his free throws. more frees throws out of 5 attempts (we assume the shots are independent). To do this, we use the digits 1, 2, and 3 to correspond to making the free throw and the digit 4 to correspond to missing the free throw. If the table of random digits begins with the digits below, how many free throw does he hit in our first simulation of five shots? 19223 95034 58301

5

Use Scenario 5-5. P(AUB)=

5/6

Use Scenario 5-11. Which of the following statements supports the conclusion that the event "Right-handed" and the event "Online" are not independent?

51/60≠166/200

You want to use simulation to estimate the probability of getting exactly one head and one tail in two tosses of a fair coin. You assign the digits 0, 1, 2, 3, 4 to heads and 5, 6, 7, 8, 9 to tails. Using the following random digits to execute as many simulations as possible, what is your estimate of the probability? 19226 95034 05756 07118

6/10

Use Scenario 5-1. Based on your simulation, the estimated probability of winning $2 in this game is

7/11

Use Scenario 5-6. The event corresponding to the system failing during one period of operation is

F and G

A box has 10 tickets in it, two of which are winning tickets. You draw a ticket at random. If it's a winning ticket, you win. If not, you get another chance, as follows: your losing ticket is replaced in the box by a winning ticket (so now there are 10 tickets, as before, but 3 of them are winning tickets). You get to draw again, at random. Which of the following are legitimate methods for using simulation to estimate the probability of winning?

I and II

A basketball player makes 2/3 of his free throws. To simulate a single free throw, which of the following assignments of digits to making a free throw are appropriate? I. 0 and 1 correspond to making the free throw and 2 corresponds to missing the free throw. II. 01, 02, 03, 04, 05, 06, 07, and 08 correspond to making the free throw and 09, 10, 11, and 12 correspond to missing the free throw. III. Use a die and let 1, 2, 3, and 4 correspond to making a free throw while 5 and 6 correspond to missing a free throw.

I, II, and III

Which of the following statements is not true?

If two events are independent, then they must be mutually exclusive.

Event A occurs with probability 0.3. If event A and B are disjoint, then

P(B) <_ 0.7

A game consists of drawing three cards at random from a deck of playing cards. You win $3 for each red card that is drawn. It costs $2 to play. For one play of this game, the sample space S for the net amount you win (after deducting the cost of play) is

S = { -$2, $1, $4, $7}

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."

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

disjoint

Use Scenario 5-3. The events A = the next two babies are boys, and B = the next two babies are girls are

disjoint

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 independent of each other

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 increases.

You read in a book on poker that the probability of being dealt three of a kind in a five-card poker hand is 1/50. What does this mean?

if you deal thousands of poker hands, the fraction of them that contain three of a kind will be very close to 1/50

When two coins are tossed, the probability of getting two heads is 0.25. This means that

in the long run two heads will occur on 25% of all tosses.

Use Scenario 5-5. The events A and B are

independent

Event A occurs with probability 0.8. The conditional probability that event B occurs, given that A occurs, is 0.5. The probability that both A and B occur

is 0.4

Use Scenario 5-6. The event corresponding to the system functioning properly during one period of operation is

not F or not G

A stack of four cards contains two red cards and two black cards. I select 2 cards one at a time, and do not replace the first card selected before selecting the second card. Consider the events A = the first card selected is red B = the second card selected is red The events A and B are

not independent, not disjoint.

Use Scenario 5-12. P(AUB) is

q + s+ r

Use Scenario 5-12. The probability associated with the intersection of A and B.

r

Use Scenario 5-12. P(B|A) is

r/q+r

If the individual outcomes of a phenomenon are uncertain, but there is nonetheless a regular distribution of outcomes in a large number of repetitions, we say the phenomenon is

random

A basketball player shoots 8 free throws during a game. The sample space for counting the number she makes is

s= whole numbers 0 to 8

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

sample space

You are playing a board game with some friends that involves rolling two six-sided dice. 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

If I toss a fair coin 5000 times

the proportion of heads will be close to 0.5

Here is an assignment of probabilities to the face that comes up when rolling a die once: Outcome 1 2 3 4 5 6 Probability 1/7 2/7 0 3/7 0 1/7 Which of the following is true?

this is a legitimate assignment of probability

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

venn diagram w box A and box B shaded

Among the students at a large university who describe themselves as vegetarians, some eat fish, some eat eggs, some eat both fish and eggs, and some eat neither fish nor eggs. Choose a vegetarian student at random. Let E = the event that the student eats eggs, and let F = the event that the student eats fish. Which of the following Venn diagrams has correctly shaded the event that the student eats neither fish nor eggs?

venn diagram w outside region shaded, boxes E and F are not shaded