Probability and Counting Principles

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.

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.

How many ways can a committee of 4 be chosen from 10 people? (Order doesn't matter)

• 120

• 210

• 5040

• 252

How would you solve?

From the 20 DVD's you purchased this past year, you plan to take five with you on vacation. How many different sets of five DVD's can you take?

• Permutation

• Combination

Find the number of possibilities:
A group of 25 people are going to run a race.  The top 8 finishers advance to finals.

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?