Probability and Counting Principles

A cube, with faces numbered 1 to 6, is rolled, and a penny is tossed at the same time. How many elements in the sample space consist of an even number and a tail?

• 12

• 2

• 3

• 4

When a fair coin was tossed ten times, it landed heads up the first seven times. What is the probability that on the eighth toss the coin will land with tails up?

Maria has a set of 10 index cards labeled with the digits 0 through 9. She puts them in a bag and selects one at random. The outcome that is most likely to occur is selecting.

• an off number

• a prime number

• a number that is at most 5

• a number that is divisible by 3.

Five students, Caroline, Ashley, Malika, Gianna, and Lily, line up one behind the other. How many different ways can they stand in line?

• 60

• 5

• 25

• 120

A lock has a 3-number code made up of 27 numbers. If none of the numbers are allowed to repeat, how many different ways can you choose three different numbers in order for a unique code?

• 3

• 19683

• 17550

• 27

A bag contains 4 red marbles, 6 blue marbles and 5 green marbles. If three marbles are drawn out of the bag, what is the exact probability that all three marbles drawn will be green?

On a given school day, the probability that Nick oversleeps is 48% and the probability he has a pop quiz is 25%. Assuming these two events are independent, what is the probability that Nick oversleeps and has a pop quiz on the same day?

• 12%

• 73%

• 36%

• 23%

Juan has three blue shirts, two green shirts, seven red shirts, five pairs of denim pants, and two pairs of khaki pants. How many different outfits consisting of one shirt and one pair of pants are possible?

• 19

• 84

• 130

• 420

How many different three-member teams can be selected from a group of seven students?

• 35

• 1

• 210

• 5040

In a class of 30 students, 13 have a cat and 10 have a dog. There are 4 students who have a cat and a dog. Draw a chart that represents the details of the question and find the probability that a student who does not have a dog has a cat.