84%test

Five students want to play dodgeball and they all want to be a team captain. To be fair, the gym coach decides to place the names of all five students into a hat, mix well, and select two names at random without replacement. The names chosen will be the team captains. Each outcome in the sample space for the random selection of two team captains is equally likely. What is the probability of each outcome in the sample space?

A. 1/25

A hair stylist knows that 87% of her customers get a haircut and 40% get their hair colored on a regular basis. Of the customers who get their hair cut, 24% also get their hair colored. What is the probability that a randomly selected customer gets their hair cut and colored? 0.10 0.21 0.35 0.40

B

The following two-way table shows the distribution of daily traffic and weather issues in a certain large city. Suppose a day from this city is selected at random. Let event A = heavy traffic and event B = bad weather. Are events A and B independent? No, P(A) = P(B|A). No, P(A) ≠ P(A|B). Yes, P(A) = P(A|B). Yes, P(A) ≠ P(B|A).

B

Four seniors and six juniors are competing for four places on a quiz bowl team. What is the approximate probability that all four seniors will be chosen at random? 0.00020 0.00476 0.06667 0.07142

B. 0.00476

Suppose that 71% of the surface of the Earth is covered in water, and a random number generator uses latitude and longitude to select a random location on the Earth. If 6 such locations are generated, what is the probability that all 6 locations are in water? 0.0006 0.1281 0.8719 0.9994

B. 0.1281

A candle shop owner collected data on customers' favorite scents, as shown in the table. A customer is randomly selected. If the probabilities of a customer choosing floral and coconut as their favorite scents are the same, what is the value of the missing probabilities? 0.10 0.14 0.20 0.28

B. 0.14

A teacher offers gift cards as a reward for classroom participation. The teacher places the gift cards from four different stores into a bag and mixes them well. A student gets to select two gift cards at random (one at a time and without replacement). Each outcome in the sample space for the random selection of two gift cards is equally likely. What is the probability of each outcome in the sample space?

B. 1/6

During final exam weeks, many college students exercise to fuel their study sessions. Data from a recent survey are shown in the Venn diagram. Let M be the event that the student exercises in the morning and let A be the event that the student exercises in the afternoon. What is the probability that a randomly chosen college student exercises in the morning or afternoon? 0.37 0.39 0.62 0.76

D. 0.76

For students majoring in Hospitality Management, it was determined that 5% have visited 1-10 states, 16% have visited 11-20 states, 45% have visited 21-30 states, 19% have visited 31-40 states, and 15% have visited 41-50 states. Suppose a Hospitality Management student is randomly selected. What is the probability that the student has visited 21 or more states? 0.15 0.21 0.45 0.79

D. 0.79

A randomly generated password contains four characters. Each of the four characters is either a lowercase letter or a digit from 0-9. Each character in the password cannot be used more than once. What is the approximate probability that exactly one of the four characters will be a number? 1% 11% 28% 44%

D. 44%

In Canada, 63% of households speak English as their primary language, and 23% speak French as their primary language. If two Canadian households are selected at random, what is the probability that the first household speaks French, but the second household speaks English? (0.23)(0.63) = 0.1449 0.23 + 0.63 = 0.86 0.23 + 0.63 - (0.23)(0.63) = 0.7451

A.

A security alarm requires a four-digit code. The code can use the digits 0-9 and the digits cannot be repeated. Which expression can be used to determine the probability of the alarm code beginning with a number greater than 7?

A. (2p1) (9p3) / (10p4)

A medical clinic is randomly selecting two staff members to attend a conference. The clinic employees include 7 nurses, 3 doctors, and 2 office staff. The nurses want to know the probability that both attendees will be nurses. The tree diagram displays the possible outcomes of randomly selecting two staff members. Which probability is represented by label 3 in the tree diagram?

A. 5/12

A researcher randomly selects 95 high school students and asks their handwriting preference and how well they dance. The two-way table displays the data. Suppose one of the students is randomly selected. Let B = the student prefers writing in block letters and F = the student's dancing skills are fair. Which of the following is the correct value and interpretation of P(B|F)? P(B|F) = 0.37; given that the student has fair dancing skills, there is a 0.37 probability that they prefer to write with block letters. P(B|F) = 0.37; given that the student prefers to write with block letters, there is a 0.37 probability that they have fair dancing skills. P(B|F) = 0.45; given that the student has fair dancing skills, there is a 0.45 probability that they prefer to write with block letters. P(B|F) = 0.45; given that the student prefers to write with block letters, there is a 0.45 probability that they have fair dancing skills.

B

A bag contains five red marbles, two orange marbles, one yellow marble, and two green marbles. Two marbles are drawn from the bag. What is the approximate probability one of the chosen marbles is orange and one of the chosen marbles is green? 0.02222 0.04444 0.08889 0.13333

B. 0.04444

Insurance company executives surveyed 200 young adults about their first motor vehicle. The results are shown in the two-way table. A survey participant is randomly selected. Let E be the event that the participant's first motor vehicle had eight cylinders and let T be the event that the participant's first motor vehicle was a truck. What is the value of P(E or T)? 0.03 0.14 0.17 0.28

B. 0.14

A cereal company hopes to increase its sales by putting prizes in randomly selected boxes of its lowest-selling children's cereal. The company claims that the probability of getting a prize is 0.75. Which is the correct interpretation of this probability? This company expects to increase cereal sales by 75%. There is a guarantee of getting 3 prizes when buying 4 boxes of this type of cereal. In many, many boxes of cereal of this type, we can expect about 75% of the boxes to contain a prize. The claim of this company is correct if exactly 75 out of 100 boxes of this type of cereal contain a prize.

C

During final exam weeks, many college students exercise to fuel their study sessions. Data from a recent survey are shown in the Venn diagram. Let M be the event that the student exercises in the morning and let A be the event that the student exercises in the afternoon. What is the probability that a randomly chosen college student does not exercise in the morning? 0.14 0.24 0.38 0.75

C. 0.38

On a certain hole, a golfer knows that he has a 70% chance of reaching the green (putting surface) in one stroke, 20% in two strokes, 8% in three, and 2% in four or more. If he reaches the green on his first stroke, he has an 80% chance of putting the golf ball in the cup on his second stroke. If he does not reach the green on his first stroke, then he has a 30% chance of putting the golf ball in the cup on his second stroke. What is the probability that the golfer will reach the green in one stroke and put the ball in the cup on his second stroke? 0.09 0.21 0.56 0.80

C. 0.56

A recent survey suggests that 47% of all televisions are connected to the internet, 32% are voice controlled, and 22% are both connected to the internet and voice controlled. Suppose a television is selected at random and it is voice controlled. What is the probability that a randomly selected voice-controlled television is also connected to the internet? 0.15 0.47 0.69 0.79

C. 0.69

Suppose that 71% of the surface of the Earth is covered in water, and a random number generator uses latitude and longitude to select a random location on the Earth. If 6 locations are generated, what is the probability that at least 1 of those locations is over land? 0.0006 0.1281 0.8719 0.9994

C. 0.8719

At the beginning of the semester, a professor tells students that if they study for the tests, then there is a 55% chance they will get a B or higher on the tests. If they do not study, there is a 20% chance that they will get a B or higher on the tests. The professor knows from prior surveys that 60% of students study for the tests. The probabilities are displayed in the tree diagram. The professor informs the class that there will be a test next week. What is the probability that a randomly selected student studied for the test if they pass it with a B or higher? 0.20 0.55 0.60 0.80

D

A researcher randomly surveyed 1,477 farmers to determine the geographical region in which they farm and the types of crops that grow there. The two-way table displays the data. Suppose a farmer from this survey is chosen at random. Let M = farmer lives in the Midwest and V = farmer grows vegetables. What is the value of P(V|M)?

D. 251/365

Shawn is playing a game with a set of cards. Half of them are blue and the other half are yellow. In the game, the player guesses the color of the top card, looks at the card, and returns the card to the deck. The player continues to do this, shuffling the deck after each guess. Shawn has guessed the first three attempts as "blue" and has been correct on each guess. He says he will guess "yellow" for the next card since a yellow card is due to happen. Is Shawn's reasoning correct? Yes, Shawn has guessed well so far, so it is clear that he cannot miss. No, all of the cards have been blue so far, so the next one must also be blue. Yes, half of the cards are yellow, so the fourth card should be yellow to compensate for the first three cards being blue. No, the law of large numbers says that the proportion of yellow cards should approach the true probability after many trials.

D. No, the law of large numbers says that the proportion of yellow cards should approach the true probability after many trials.

Insurance company executives surveyed 200 young adults about their first motor vehicle. The results are shown in the two-way table. A survey participant is randomly selected. Let F be the event that the participant's first motor vehicle had four cylinders and let U be the event that the participant's first motor vehicle was an SUV. What is the value of P(FC and U)? 0.09 0.10 0.11 0.22

NOT A, maybe C