Estimating Probabilities of Compound Events

Matilda is spinning a spinner with eight equal-sized sections numbered 1 through 8. She spins the spinner two times. What is the probability that Matilda's first spin will be an odd number and her second spin will be a number less than 3?

• 1/8

• 3/16

• 1/64

• 3/4

Trina is buying a two-scoop ice cream cone. She can choose from the flavors vanilla (V), chocolate (C), strawberry (S), and peppermint (P). She makes a tree diagram to represent the sample space. Trina randomly chooses two scoops of ice cream. If each flavor is equally likely to be chosen, what is the probability that she chooses two scoops of the same flavor?

• 1/2

• 1/4

• 1/3

• 4/20

A principal determines there is a 10% chance that a student entering the school store will make a purchase. Petra wants to know the probability that at least 2 of the first 40 students visiting the school store when she works there will make a purchase. Petra will put 1 blue marble and 9 yellow marbles into a bag. She will draw a marble, record the color, and replace it 40 times for each trial. She will run 20 trials, and find the fraction of times at least 2 blue marbles are drawn. Which explains whether or not Petra's simulation for estimating the probability is reasonable?

• Petra's simulation is not reasonable, because she should draw and replace a marble 10 times for 40 trials instead of 40 times for 20 trials.

• Petra's simulation is not reasonable, because the marbles do not appropriately represent the probabilities of a visitor making a purchase. She should use 2 blue marbles and 38 yellow marbles instead.

• Petra's simulation is reasonable, and she can also use the number of times at least 38 yellow marbles are drawn as a favorable outcome for estimating probabilities.

• Petra's simulation is reasonable, and she can also run more than 20 trials to gather data for estimating the probability.

On a game show, players roll two standard cubes. The sum of the number cubes times 100 determines the number of points they will win. What is the probability of winning at least 900 points?

• 1/9

• 5/36

• 5/18

• 7/36

Alejandro is spinning a spinner with six equal-sized sections numbered 1 through 6. He spins the spinner two times. What is the probability that Alejandro will not land on the numbers 2 or 4 on either spin?

• 1/18

• 5/9

• 4/9

• 2/3

You ask the salesperson at a pizza place to give you a pizza with any two​ toppings, but the toppings must be different. The choices are shown in the table. Use a table to show the sample space. Then find the probability of getting a pizza with broccoli and olives.

• 1/30

• 1/15

• 3/30

• 3/5

All possible outcomes of spinning the pointers of two spinners with​ equal-sized sections labeled 1 through 3 are recorded in the table. Find the probability that the sum of the numbers shown on each spinner will be greater than or equal to 5.

• 1/3

• 4/9

• 1/9

• 2/3

The organized list shows all the possible outcomes when three fair coins are flipped. The possible outcomes of each flip are heads​ (H) and tails​ (T). What is the probability that exactly 1 fair coin lands heads up when 3 are​ flipped?

• 1/4

• 3/8

• 1/2

• 5/8

The table shows the possible outcomes of spinning the given spinner and tossing a fair coin. Find the probability of​ P(1,H).

• 1/10

• 1/5

• 1/4

• 1/2

The tree diagram shows all the possible varieties of a​ T-shirt available in​ small, medium, and large and in the colors blue and yellow. What is the probability that a medium​ T-shirt or a yellow​ T-shirt is randomly​ selected?

• 1/6

• 1/3

• 1/2

• 2/3