Probability and Statistics Quiz

A survey was taken of children between the ages of 3 and 7. Let A be the event that the person has 2 siblings, and let B be the event that the person does not have a pet. Which statement is true about whether A and B are independent events?

• A and B are independent events because P(A∣B) = P(A) = 0.18.

• A and B are independent events because P(A∣B) = P(A) = 0.4.

• A and B are not independent events because P(A∣B) = 0.4 and P(A) = 0.18.

• A and B are not independent events because P(A∣B) = 0.18 and P(A) = 0.4.

The two-way table shows the number of sport utility vehicles with certain features for sale at the car lot. What is the probability that a randomly selected car with no 4-wheel drive has third-row seats?

• 0.3

• 0.4

• 0.7

• 0.8

People at the state fair were surveyed about which type of lemonade they preferred. The results are shown below. Pink lemonade: 156 males, 72 females Yellow lemonade: 104 males, 48 females The events 'prefers pink lemonade' and 'female' are independent because

• P(pink lemonade | female) = P(pink lemonade) = 0.6.

• P(female | pink lemonade ) = P(pink lemonade) = 0.3.

• P(pink lemonade | female) = 0.3 and P(pink lemonade) = 0.6.

• P(female | pink lemonade ) = 0.3 and P(pink lemonade) = 0.6.

Fifty-five percent of the members of the junior varsity swim team wear glasses. Of the team members who do not wear glasses, 30 percent of them are in the 10th grade. To the nearest whole percent, what is the probability that a randomly chosen member of the JV swim team does not wear glasses and is in the 10th grade?

• 14%

• 17%

• 55%

• 67%

The probability for event A is 0.3, the probability for event B is 0.6, and the probability of events A or B is 0.8. Why are the events not mutually exclusive?

• The sum of P(A) and P(B) is less than P(A or B).

• The product of P(A) and P(B) is less than P(A or B).

• The product of P(A) and P(B) is not equal to P(A or B).

• The sum of P(A) and P(B) is not equal to P(A or B).

A guidance counselor reports that in a given semester, the probability that a student chooses art as an elective is 15 percent, the probability that a student chooses art or drama is 20 percent, and the probability that a student chooses both art and drama is 2 percent. What is the probability that a student chooses drama as an elective?

• 5 percent

• 7 percent

• 33 percent

• 37 percent

Four speed skaters, Marco, Naim, Oliver, and Pedro, compete in a relay race where they all agree that Naim will be the last skater. Then, they try to decide whether or not Oliver should be the first skater in the race. Which subset, A, of the sample space shows the complement of the event in which Oliver is the first skater in the race?

• A = {MOPN, PMON}

• A = {OPMN, OMPN}

• A = {MOPN, MPON, OPMN, POMN}

• A = {MOPN, MPON, PMON, POMN}

A four-person committee is chosen from a group of eight boys and six girls. If students are chosen at random, what is the probability that the committee consists of all boys?

• 4/1001

• 15/1001

• 10/143

• 133/143

Iliana is painting a picture. She has green, red, yellow, purple, orange, and blue paint. She wants her painting to have four different colors. If order does not matter, in how many ways can she pick four colors if green must be one of them?

• 4

• 6

• 10

• 15

Including Jose, there are eight people in his family. If order matters, how many ways can he arrange his family members into a row of five seats if Jose must sit in the first seat?

• 35

• 840

• 1,680

• 2,620