12.3 Notes

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12.3 Probability

Vocabulary

Probability: a ratio that measures the chances of an event occurring.

Odds:

  a ratio of success to failures (odds of success) a ratio of failures to success (odds of failure)  Failure: any other outcome  Success: a desired outcome

Vocabulary Continued

Random: when all outcomes have

an equally likely chance of occuring 

Random Variable: a variable

whose value is the numerical outcome of a random event

KEY CONCEPTS

Probability of Success: If an event can succeed in s ways (will occur)

P

(

S

) 

s

s f

Probability of Failure: If an event can fail in f ways (will not occur)

P

(

F

) 

s

f f

Examples

 What’s the probability of flipping a coin and having it land on heads?

Examples

 6 Find the odds of an event occurring, given the probability of an event.

6 13 5 12 13 1 8 5 12 1 8

Examples

 Find the probability of an event occurring, given the odds of the event 12 : 1 4 : 5 8 : 9

 If there are 18 marbles in a bag and 3 are red and 4 are green, 3 are white, and 8 are blue what’s the probability of choosing:  A red marble  A green marble  Not picking a white marble  Not picking a blue marble

Probability with Combinations and Permutations

 Follow these steps: 1. Write the combination or permutation for the first group 2. Multiply by the combination or permutation for the second group 3. Divide the product by the total combinations or permutations possible 4. Write a fraction for the probability

Monica has a collection of 32 CD’s- 18 R&B and 14 rap. As she is leaving for a trip, she randomly chooses 6 CD’s to take with her. What is the probability that she selects 3 R&B and 3 rap?

A board game is played with tiles and letters on one side. There are 56 tiles with consonants and 42 tiles with vowels. Each player must choose seven of the tiles at the beginning of the game. What is the probability that a player selects four consonants and three vowels?

Ramon has five books on the floor, one for each of his classes: Algebra 2, Chemistry, English, Spanish, and History. Ramon is going to put the books on a shelf. If he picks the books up at random and places them ina row on the same shelf, what is the probability that his English, Spanish, and Algebra 2 books will be the leftmost books on the shelf, but not necssarily in that order?

For next semester, Alisa has signed up for English, Precalculus, Spanish, Geography, and chemistry classes. If class schedules are assigned randomly and each class is equally likely to be at any time of day what is the probability that Alisa’s first two classes in the morning will be Precalculus and Chemistry, in either order?

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