Probability

The faces of a four-sided fair die are numbered 1 through 4, respectively. For a certain game, the die is tossed and the number that lands facedown is recorded. The table below summarizes the points a player earns for the number that lands facedown. Consider two independent tosses of the die. Let the random variable S represent the sum of the points earned from the two tosses. Which table represents the probability distribution of S ?

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A contestant’s final winnings on a game show are determined by a random selection of a base amount and a possible multiplier. For the base amount, the contestant randomly selects one of four cards, where two cards are marked $1,000, one card is marked $2,000, and one card is marked $5,000. After choosing the card, the contestant randomly selects one of five chips, where three chips are red and two chips are white. If the selected chip is red, the contestant’s final winnings are twice the value of the base amount. If the selected chip is white, the contestant’s final winnings are the value of the base amount. What is the probability that a contestant’s final winnings are exactly $2,000?

• 0.100

• 0.200

• 0.250

• 0.325

• 0.400

Tags

CCSS.HSS.MD.B.5A

The SC Electric Company has bid on two electrical wiring jobs. The owner of the company believes that

the probability of being awarded the first job (event A) is 0.75;

the probability of being awarded the second job (event B) is 0.5;

and the probability of being awarded both jobs (event (A and B)) is 0.375.

If the owner’s beliefs are correct, which of the following statements must be true concerning event A and event B ?

• Event A and event B are mutually exclusive and are independent.

• Event A and event B are mutually exclusive and are not independent.

• Event A and event B are not mutually exclusive and are independent.

• Event A and event B are not mutually exclusive and are not independent.

• Event A and event B are not mutually exclusive, and independence cannot be determined with the information given.

Tags

CCSS.HSS.CP.A.2

CCSS.HSS.CP.A.4

Ali surveyed 200 students at a school and recorded the eye color and the gender of each student. Of the 80 male students who were surveyed, 60 had brown eyes. If eye color and gender are independent, how many female students surveyed would be expected to have brown eyes?

• 5

• 20

• 30

• 90

• 100

Tags

CCSS.HSS.CP.A.2

CCSS.HSS.CP.A.4

A blind taste test will be conducted with 9 volunteers to determine whether people can taste a difference between bottled water and tap water. Each participant will taste the water from two different glasses and then identify which glass he or she thinks contains the tap water. Assuming that people cannot taste a difference between bottled water and tap water, what is the probability that at least 8 of the 9 participants will correctly identify the tap water?

• 0.0020

• 0.0195

• 0.8889

• 0.9805

• 0.9980

Ms. Tucker travels through two intersections with traffic lights as she drives to the market. The traffic lights operate independently. The probability that both lights will be red when she reaches them is 0.22. The probability that the first light will be red and the second light will not be red is 0.33. What is the probability that the second light will be red when she reaches it?

• 0.40

• 0.45

• 0.50

• 0.55

• 0.60

The distribution of colors of candies in a bag is as follows. If two candies are randomly drawn from the bag with replacement, what is the probability that they are the same color?

• 0.09

• 0.22

• 0.25

• 0.75

• 0.78

For flights from a particular airport in January, there is a 30 percent chance of a flight being delayed because of icy weather. If a flight is delayed because of icy weather, there is a 10 percent chance the flight will also be delayed because of a mechanical problem. If a flight is not delayed because of icy weather, there is a 5 percent chance that it will be delayed because of a mechanical problem. If one flight is selected at random from the airport in January, what is the probability that the flight selected will have at least one of the two types of delays?

• 0.065

• 0.335

• 0.350

• 0.450

• 0.665

Tags

CCSS.HSS.CP.B.7

The XYZ Office Supplies Company sells calculators in bulk at wholesale prices, as well as individually at retail prices. Next year's sales depend on market conditions, but executives use probability to find estimates of sales for the coming year. The following tables are estimates for next year's sales. What profit does XYZ Office Supplies Company expect to make for the next year if the profit from each calculator sold is $20 at wholesale and $30 at retail.

• $10,590

• $220,700

• $264,750

• $833,100

• $1,002,500

Tags

CCSS.HSS.MD.A.2

A manufacturer makes lightbulbs and claims that their reliability is 98 percent. Reliability is defined to be the proportion of non-defective items that are produced over the long term. If the company's claim is correct, what is the expected number of non-defective lightbulbs in a random sample of 1,000 bulbs?

• 20

• 200

• 960

• 980

• 1,000

Tags

CCSS.7.SP.C.6