Multiplication Rule Probability

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?

• $\frac{1}{22}$

• $\frac{6}{11}$

• $\frac{9}{16}$

• $\frac{21}{22}$

There are 9 movies showing at a theater. Two are action movies, two are children’s movies, and the other movies are comedies. Ashley randomly selects 2 different movies to see. What is the probability that the first movie is an action movie and the second movie is a comedy?

• $\frac{1}{18}$

• $\frac{10}{81}$

• $\frac{5}{36}$

• $\frac{7}{9}$

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?

• $\frac{3}{20}$

• $\frac{1}{6}$

• $\frac{15}{56}$

• $\frac{8}{15}$

An experiment consists of spinning a spinner and flipping a fair coin. The spinner consists of 4 colored sections of equal size.

• Red

• Blue

• Green

• Yellow

If the arrow on the spinner is spun one time and the coin flipped one time, what is the probability of getting the outcome “Blue, Tails”?

• $\frac{1}{8}$

• $\frac{1}{6}$

• $\frac{1}{4}$

• $\frac{3}{4}$

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?

• $\frac{1}{200}$

• $\frac{29}{200}$

• $\frac{171}{200}$

• $\frac{199}{200}$

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?

• $\frac{1}{120}$

• $\frac{1}{57}$

• $\frac{15}{343}$

• $\frac{3}{20}$

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?

• $\frac{1}{60}$

• $\frac{5}{144}$

• $\frac{5}{12}$

• $\frac{47}{60}$

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?

• $\left(\frac{9}{10}\right)\times\left(\frac{8}{9}\right)\times\left(\frac{1}{8}\right)$

• $\left(\frac{9}{10}\right)\times\left(\frac{8}{9}\right)\times\left(\frac{7}{8}\right)$

• $\left(\frac{9}{10}\right)\times\left(\frac{8}{9}\right)\times\left(\frac{1}{10}\right)$

• $\left(\frac{9}{10}\right)\times\left(\frac{8}{9}\right)\times\left(\frac{7}{10}\right)$