Milestone 3

Using this Venn diagram, what is the probability that event A or event B occurs? 0.41 0.36 0.68 0.77 RATIONALE

0.77

There is a 30% chance of rain tomorrow. What are the odds in favor of it raining? 3:7 3:10 7:3 10:3

3:7

Kate was trying to decide which type of frozen pizza to restock based on popularity: pepperoni pizza or sausage pizza. After studying the data, she noticed that pepperoni flavors sold best on the weekdays and on the weekends, but not best overall. Which paradox has Kate encountered? Benford's Law False Negative False Positive Simpson's Paradox

Simpson's Paradox

John makes random guesses on his multiple-choice test, which has five options for each question. Let the random variable X be the number of guesses taken before guessing correctly. Assuming the guesses are independent, find the probability that he doesn't guess correctly until his 6th guess. 0.0789 0.0655 0.3521 0.3277

0.0655

The average number of babies born at a private hospital's maternity wing is 6 per hour.What is the probability that three babies are born during a particular 1-hour period in this maternity wing? 0.16 0.13 0.09 0.20

0.09

A survey asked 1,000 people which magazine they preferred, given three choices. The table below breaks the votes down by magazine and age group. Age Below 40 Age 40 and Above The National Journal 104 200 Newsday 120 230 The Month 240 106 If a survey is selected at random, what is the probability that the person voted for "Newsday" and is also age 40 or older? Answer choices are rounded to the hundredths place. 0.23 0.54 0.66 0.34

0.23

Three hundred students in a school were asked to select their favorite fruit from a choice of apples, oranges, and mangoes. This table lists the results. BoysGirlsApple6646Orange5241Mango4055 If you were to choose a boy from the group, what is the probability that mangoes are his favorite fruit? Answer choices are rounded to the hundredths place. 0.75 0.39 0.13 0.25

0.25

Maria flipped a coin 60 times, and the coin came up tails 32 times. What is the relative frequency of the coin turning up heads in this experiment? Answer choices are rounded to the hundredths place. 0.47 2.14 1.88 0.53

0.47

Using the Venn Diagram below, what is the conditional probability of event B occurring, assuming event A has happened [P(B|A)]? 0.63 0.24 0.41 0.77

0.63

David is playing a game where he flips two coins and counts the total number of heads. The possible outcomes and probabilities are shown in the probability distribution below. What is the expected value for the number of heads from flipping two coins? 3 2 1.5 1

1

A magician asks an audience member to pick any number from 6 to 15. What is the theoretical probability that an individual chooses the number the magician has in mind? 1 over 9 6 over 15 1 over 10 1 over 15

1 over 10

What is the probability of NOT drawing a face card from a standard deck of 52 cards. 8 over 13 3 over 13 10 over 13 1 half

10 over 13

The gender and age of Acme Painting Company's employees are shown below. Age Gender 23 Female 23 Male 24 Female 26 Female 27 Male 28 Male 30 Male 31 Female 33 Male 33 Female 33 Female 34 Male 36 Male 37 Male 38 Female 40 Female 42 Male 44 Female If the CEO is selecting one employee at random, what is the chance he will select a male OR someone in their 40s? 1/18 1/2 11/18 1/3

11/18

Phil is randomly drawing cards from a deck of 52. He first draws a Queen, places it back in the deck, shuffles the deck, and then draws another card. What is the probability of drawing a Queen, placing it back in the deck, and drawing any face card? Answer choices are in the form of a percentage, rounded to the nearest whole number. 2% 25% 7% 31%

2%

Mark noticed that the probability that a certain player hits a home run in a single game is 0.165. Mark is interested in the variability of the number of home runs if this player plays 150 games. If Mark uses the normal approximation of the binomial distribution to model the number of home runs, what is the variance for a total of 150 games? Answer choices are rounded to the hundredths place. 0.91 4.55 24.75 20.67

20.67

Luke went to a blackjack table at the casino. At the table, the dealer has just shuffled a standard deck of 52 cards. Luke has had good luck at blackjack in the past, and he actually got three blackjacks with Queens in a row the last time he played. Because of this lucky run, Luke thinks that Queens are the luckiest card. The dealer deals the first card to him. In a split second, he can see that it is a face card, but he is unsure if it is a Queen. What is the probability of the card being a Queen, given that it is a face card? Answer choices are in a percentage format, rounded to the nearest whole number. 77% 4% 8% 33%

33%

Ryan is playing a multiplication game with a pile of 26 cards, each with a number on them. Each turn, he flips over two of the cards, and has to multiply the numbers. How many possible outcomes are there on Ryan's first turn flipping two cards? 52 676 26 650

650

Satara was having fun playing poker. She needed the next two cards dealt to be hearts so she could make a flush (five cards of the same suit). There are 10 cards left in the deck, and three are hearts. What is the probability that the two cards dealt to Satara (without replacement) will both be hearts? Answer choices are in percentage format, rounded to the nearest whole number. 26% 7% 60% 30%

7%

Zhi and her friends moved on to the card tables at the casino. Zhi wanted to figure out the probability of drawing a black Queen or a black Jack. Choose the correct probability of drawing a black Queen or a black Jack. Answer choices are in the form of a percentage, rounded to the nearest whole number. 15% 4% 8% 25%

8%

Which of the following situations describes a continuous distribution? A probability distribution showing the amount of births in a hospital in a month A probability distribution showing the number of vaccines given to babies during their first year of life A probability distribution showing the weights of newborns A probability distribution showing the average number of days mothers spent in the hospital

A probability distribution showing the weights of newborns

Sadie is selecting two pieces of paper at random from the stack of colored paper in her closet. The stack contains several sheets of each of the standard colors: red, orange, yellow, green, blue, and violet. All of the following are possible outcomes for Sadie's selection, EXCEPT: Blue, black Orange, yellow Green, violet Red, red

Blue, black

Joseph selects a card from a standard deck of 52 cards and then replaces it afterwards. He decides to record the total number of red cards that he selects and calculates the proportion of red cards that he has selected so far after each pick. He then constructs a graph to visualize his results. Which of the following statements is FALSE? The theoretical probability for selecting a red card in each pick is 0.5. For a given number of selections, we can use Joseph's graph to find the number of diamonds that he has picked so far. This is an example of the law of large numbers. The relative frequency of selecting a red card changes with the increase in number of selections.

For a given number of selections, we can use Joseph's graph to find the number of diamonds that he has picked so far.

Select the following statement that describes non-overlapping events. To win, Jon needs a red card. He receives a Queen of Diamonds. Receiving the King of Hearts fulfills Jon's need of getting both a face card and a heart. Jon needs to roll an even number to win. When it's his turn, he rolls a two. Jon wants a face card so he can have a winning hand, and he receives the eight of clubs.

Jon wants a face card so he can have a winning hand, and he receives the eight of clubs.

Two sets A and B are shown in the Venn diagram below. Which statement is TRUE? Sets A and B have 3 common elements. There are a total of 2 elements shown in the Venn diagram. Set B has 7 elements. Set A has 8 elements.

Sets A and B have 3 common elements.

Which of the following is an example of a false positive? Test results confirm that a patient has cancer. Test results indicate that a patient has cancer when, in fact, he does not. Test results indicate that a patient does not have cancer when, in fact, he does. Test results confirm that a patient does not have cancer.

Test results indicate that a patient has cancer when, in fact, he does no

A bag holds 20 red marbles and 40 green ones, for a total of 60 marbles. Ryan picks one marble from the bag at random, hoping to pick a red marble. Which of the following statements is true? The probability that Ryan will pick a red marble on the first try is 33%. If he keeps this marble and picks another from the bag, the probability that he will pick a green marble decreases. The probability that Ryan will pick a red marble on the first try is 33%. If he keeps this marble and picks another from the bag, the probability that he will pick a green marble increases. The probability that Ryan will pick a red marble on the first try is 67%. If he keeps this marble and picks another from the bag, the probability that he will pick a green marble increases. The probability that Ryan will pick a red marble on the first try is 67%. If he keeps this marble and picks another from the bag, the probability that he will pick a green marble decreases.

The probability that Ryan will pick a red marble on the first try is 33%. If he keeps this marble and picks another from the bag, the probability that he will pick a green marble increases.

Which of the following is a property of binomial distributions? All trials are dependent. The sum of the probabilities of successes and failures is always 1. The expected value is equal to the number of successes in the experiment. There are exactly three possible outcomes for each trial.

The sum of the probabilities of successes and failures is always 1.