Quiz about Applying the Multiplication Rule for Probability

Question 1

A key ring has 12 keys, 3 of which open the house door. If two keys are randomly selected without replacement, what is the probability that neither key opens the door?

Accepted Answer

$$\frac{6}{11}$$

Answer

$$\frac{1}{22}$$

Answer

$$\frac{9}{16}$$

Answer

$$\frac{21}{22}$$

Question 2

Sonia has 5 yellow hair clips, 2 red hair clips, and 3 blue hair clips in her purse. What is the probability that she will randomly select one yellow hair clip and one blue hair clip without replacement?

Accepted Answer

$$\frac{1}{6}$$

Answer

$$\frac{3}{20}$$

Answer

$$\frac{15}{56}$$

Answer

$$\frac{8}{15}$$

Question 3

A store has 20 boxes of cereal A and 10 boxes of cereal B. One box of each kind of cereal has a prize. If one box of each kind is randomly selected, what is the probability that neither box has a prize?

Accepted Answer

$$\frac{171}{200}$$

Answer

$$\frac{1}{200}$$

Answer

$$\frac{29}{200}$$

Answer

$$\frac{199}{200}$$

Question 4

Anna has a bag of marbles for her little sister. It contains 12 red marbles, 6 white marbles, and 2 blue marbles. She drops the bag and three marbles roll out. What is the probability that all 3 marbles are white?

Accepted Answer

$$\frac{1}{57}$$

Answer

$$\frac{1}{120}$$

Answer

$$\frac{15}{343}$$

Answer

$$\frac{3}{20}$$

Question 5

A bag contains 5 red marbles, 4 blue marbles, and 3 green marbles. Joshua will select a marble at random, record its color, and then put the marble back in the bag. He will select three marbles in this way. What is the probability that Joshua will first get a red marble, then a blue marble, and then a green marble?

Accepted Answer

$$\frac{5}{144}$$

Answer

$$\frac{1}{60}$$

Answer

$$\frac{5}{12}$$

Answer

$$\frac{47}{60}$$

Question 6

Natasha wants to unlock the supply cabinet in her office. She has 10 cabinet keys and knows that only one of these keys will unlock the supply cabinet. If she randomly selects a key without replacement, which expression represents the probability that the third key selected will unlock the supply cabinet?

Accepted Answer

$$\left(\frac{9}{10} ight) imes\left(\frac{8}{9} ight) imes\left(\frac{1}{8} ight)$$

Answer

$$\left(\frac{9}{10} ight) imes\left(\frac{8}{9} ight) imes\left(\frac{7}{8} ight)$$

Answer

$$\left(\frac{9}{10} ight) imes\left(\frac{8}{9} ight) imes\left(\frac{1}{10} ight)$$

Answer

$$\left(\frac{9}{10} ight) imes\left(\frac{8}{9} ight) imes\left(\frac{7}{10} ight)$$

Question 7

John has seven keys on a ring. He gives these keys to his friend Robin and asks her to unlock a door. If two of the seven keys can unlock the door, what is the probability that Robin unlocks the door on exactly her third attempt?

Accepted Answer

$$\frac{40}{210}$$

Answer

$$\frac{50}{210}$$

Answer

$$\frac{40}{343}$$

Answer

$$\frac{50}{343}$$

Question 8

A stack of magazines has 5 news magazines and 10 sports magazines. Two magazines are drawn at random without replacement. What is the probability of selecting a news magazine first and then a sports magazine?

Accepted Answer

$$\frac{5}{21}$$

Answer

$$\frac{1}{5}$$

Answer

$$\frac{3}{14}$$

Answer

$$\frac{2}{9}$$

Question 9

Carlos has a spinner that is divided into 3 equal-sized sectors numbered from 1 to 3, and a number cube labeled from 1 to 6. He will spin the arrow of the spinner and roll the number cube one time. What is the probability that the arrow will land on a sector labeled 3, and the number cube will land on a number less than 3?

Accepted Answer

$$\frac{1}{9}$$

Answer

$$\frac{2}{9}$$

Answer

$$\frac{2}{3}$$

Answer

$$\frac{5}{6}$$

Question 10

Two spinners are each divided into equal sections, as shown above. Each spinner is spun once. What is the probability that the spinners will land on 2 numbers with a sum of 3.5?

Accepted Answer

$$\frac{1}{24}$$

Answer

$$\frac{1}{10}$$

Answer

$$\frac{5}{12}$$

Answer

$$\frac{1}{2}$$

Question 11

A box of stickers contains 25 gold stars, 75 red stars, and 50 blue stars, all of the same size. In two random selections, what is the probability of selecting a blue star, replacing it, and then selecting a blue star again?

Accepted Answer

$$\frac{1}{9}$$

Answer

$$\frac{1}{6}$$

Answer

$$\frac{1}{4}$$

Answer

$$\frac{2}{3}$$

Question 12

A computer program randomly generates two different whole numbers from 1 to 50. If the program is run once, what is the probability that the sum of the two numbers generated is exactly 3?

Accepted Answer

$$\frac{1}{1225}$$

Answer

$$\frac{1}{2450}$$

Answer

$$\frac{1}{97}$$

Answer

$$\frac{3}{100}$$

Question 13

Brad has a bag containing 8 green cubes, 6 red cubes, and 14 yellow cubes. All of the cubes are the same size. What is the probability of randomly selecting 1 yellow cube and then 1 green cube from the bag, without replacing the first cube?

Accepted Answer

$$\frac{4}{27}$$

Answer

$$\frac{1}{112}$$

Answer

$$\frac{13}{54}$$

Answer

$$\frac{2}{5}$$

Question 14

In her book bag, Jackie has one red pencil, one yellow pencil, one blue pencil, one green pencil, one orange pencil, and one purple pencil. She also has one red pen, one blue pen, and one black pen. If Jackie randomly selects one pencil and one pen, what is the probability that she will select a purple pencil and a black pen?

Accepted Answer

$$\frac{1}{18}$$

Answer

$$\frac{1}{72}$$

Answer

$$\frac{1}{10}$$

Answer

$$\frac{1}{2}$$

Question 15

The spinner below is divided into 4 equal parts. It is spun once, and the coin is flipped once. What is the probability of obtaining red on the spinner followed by heads on the coin?

Accepted Answer

$$\frac{1}{8}$$

Answer

$$\frac{1}{4}$$

Answer

$$\frac{3}{4}$$

Answer

$$\frac{7}{8}$$

Question 16

Brent has a shopping bag with 8 similar size containers of yogurt: 2 strawberry, 3 cherry, and 3 raspberry. If he randomly takes 2 yogurt containers from the bag without replacement, what is the probability that neither will be strawberry yogurt?

Accepted Answer

$$\frac{15}{28}$$

Answer

$$\frac{1}{28}$$

Answer

$$\frac{13}{28}$$

Answer

$$\frac{27}{28}$$

Question 17

Nick randomly selects a digit from the set {0, 1, 2, ..., 9} and a letter from the set {A, B, C, ..., Z}. Matthew will try to guess both the digit and the letter. Which expression gives the probability that Matthew will incorrectly guess both the digit and the letter?

Accepted Answer

$$\frac{9}{10} imes\frac{25}{26}$$

Answer

$$\frac{1}{10}+\frac{1}{26}$$

Answer

$$\frac{1}{10} imes\frac{1}{26}$$

Answer

$$\frac{9}{10}+\frac{25}{26}$$

Question 18

The numbers 7 through 14 are written on eight cards and placed in a box. Two cards are drawn without replacement. What is the probability the 10 is drawn first, followed by the 8?

Accepted Answer

$$\frac{1}{56}$$

Answer

$$\frac{1}{4}$$

Answer

$$\frac{2}{7}$$

Answer

$$\frac{1}{42}$$

Applying the Multiplication Rule for Probability

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