Chapter 5 Math review

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

. 0.03125.

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

0.575

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 5-13. 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

Suppose we roll two six-sided dice--one red and one green. Let A be the event that the number of spots showing on the red die is three or less and B be the event that the number of spots showing on the green die is three or more. Use Scenario 5-5. P(A upside down U B) =

1/3

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

1/36

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

sample space

. Each day, Mr. Bayona chooses a one-digit number from a random number table to decide if he will walk to work or drive that day. The numbers 0 through 3 indicate he will drive, 4 through 9 mean he will walk. If he drives, he has a probability of 0.1 of being late. If he walks, his probability of being late rises to 0.25. Let W = Walk, D = Drive, L = Late, and NL = Not Late. Which of the following tree diagrams summarizes these probabilities?

tree:.6 and then .4

To simulate a toss of a coin we let the digits 0, 1, 2, 3, and 4 correspond to a head and the digits 5, 6, 7, 8, and 9 correspond to a tail. Consider the following game: We are going to toss the coin until we either get a head or we get two tails in a row, whichever comes first. If it takes us one toss to get the head we win $2, if it takes us two tosses we win $1, and if we get two tails in a row we win nothing. Use the following sequence of random digits to simulate this game as many times as possible: 12975 13258 45144 Use Scenario 5-1. Based on your simulation, the estimated probability of winning nothing is

2/11

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—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%.

Scenario 5-5 Suppose we roll two six-sided dice--one red and one green. Let A be the event that the number of spots showing on the red die is three or less and B be the event that the number of spots showing on the green die is three or more. Use Scenario 5-5. P(A B) =

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

To simulate a toss of a coin we let the digits 0, 1, 2, 3, and 4 correspond to a head and the digits 5, 6, 7, 8, and 9 correspond to a tail. Consider the following game: We are going to toss the coin until we either get a head or we get two tails in a row, whichever comes first. If it takes us one toss to get the head we win $2, if it takes us two tosses we win $1, and if we get two tails in a row we win nothing. Use the following sequence of random digits to simulate this game as many times as possible: 12975 13258 45144 Use Scenario 5-1. Based on your simulation, the estimated probability of winning $2 in this game is

7/11

. 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.

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

P(B) _<0.7.

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

. 0.875.

If I toss a fair coin 5000 times

. the proportion of heads will be close to 0.5

Suppose that A and B are independent events with and . is (PupsidedownUB^C)

.12

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

.2

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

.20

A student is chosen at random from the River City High School student body, and the following events are recorded: Use Scenario 5-8. What is the probability that the selected student is a male and ate breakfast?

.32

Use Scenario 5-2. 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: Use Scenario 5-8. What is the probability that the student had breakfast?

.5

Suppose that A and B are independent events with and . is: P(AUB)

.52

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

.64

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

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

0.02097

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 5-11. 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

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

1/4

An assignment of probabilities must obey which of the following?

All three of the above.

. 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?

E. 0.75

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?

E. I, II, and III

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.

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."

Here is an assignment of probabilities to the face that comes up when rolling a die once: Which of the following is true?

This is a legitimate assignment of probability.

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

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

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

Suppose we roll two six-sided dice--one red and one green. Let A be the event that the number of spots showing on the red die is three or less and B be the event that the number of spots showing on the green die is three or more. ____ 30. 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

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