Ch. 1 and 6 Notes Pages 20 and 21P20 1.6: Probability P21 6.7: Permutations

and Combinations

Experimental Probability

Experimental Probability: Based on observation of actual events, tests, or experiments.

trialsofnumber occursevent favorable the timesofnumber P

Example:

A quarterback throws 40 passes during a game. Thirty of the passes are completed. Find the experimental probability of the quarterback completing a pass.

Theoretical Probability

Theoretical Probability: Based on what would happen in theory.

outcomes possible ofnumber outcomes favorable ofnumber P

Example:

Find the theoretical probability of rolling a prime number when you roll a regular six-sided die.

rolled becan that numbers of #rolled becan that numbers prime of #P

Page 21 PermutationsExample: Jon, Emily, Dan, Megan, and Stephanie are running for student council. The offices are President, Vice President, and Secretary. How many ways can these five students fill the positions?

President Vice President Secretary

J

E

D

M

S

Permutations

Number of permutations: The number of ways that n items can be arranged r at a time. ORDER MATTERS!

!!rnn

Prn

Example: Jon, Emily, Dan, Megan, and Stephanie are running for student council. The offices are President, Vice President, and Secretary. How many ways can these five students fill the positions?

Notice that we can accomplish the same thing using the Multiplication Counting Principle.

Combinations

Number of combinations: The number of ways that n items can be arranged r at a time. ORDER DOES NOT MATTER!

!!!rnr

nCrn

Divides out possibilities that are the same items in a different order

Example: A pizza menu offers 6 different toppings. How many ways can you choose 4 toppings for your pizza?

Examples!!!

1. You have 7 different textbooks: Latin, French, History, Geography, Math, Physics, and Chemistry. How many different ways can you arrange them on your shelf in your bedroom?

2. You have 7 differently colored tiles. How many ways can you choose 3 of them?

3. You have 6 friends. How many ways can you choose 4 of them to walk with you to lunch?

4. How many ways can you turn up 3 cards in order from a deck of 52 cards?

5. How many different six-letter arrangements of the letters in the word SPREAD begin with R and end with S, or begin with S and end with R?

Challenge…

P20 1.6: Probability P21 6.7: Permutations

and Combinations

HW #18 1.6: P42 #1, 6, 7, 10, 15, 17

6.7: P348 #1, 2, 5, 6, 10-13, 18- 24, 29-32, 40, 46-49, 56