Probability

OBJECTIVE

Find the probability of a simple event.

Differentiate between theoretical and experimental probability.

Vocabulary

experimenttrialoutcomesample spaceeventprobabilityimpossiblecertain

An experiment is an activity in which results are observed. Each observation is called a trial, and each result is called an outcome. The sample space is the set of all possible outcomes of an experiment.

Experiment Sample Space

flipping a coin heads, tails

rolling a number cube 1, 2, 3, 4, 5, 6

guessing the number of whole numbers jelly beans in a jar

An event is any set of one or more outcomes. The probability of an event, written P(event), is a number from 0 (or 0%) to 1 (or 100%) that tells you how likely the event is to happen.

• A probability of 0 means the event is impossible, or can never happen.

• A probability of 1 means the event is certain, or has to happen.

• The probabilities of all the outcomes in the sample space add up to 1.

0 0.25 0.5 0.75 1

0% 25% 50% 75% 100%

Impossible Equally likely Certain as unlikely

14

12

340 1

• Experimental Probability – the likelihood that an event will occur based on data that has been collected. P(event) =

• Theoretical Probability – the likelihood that an event will occur based on what should happen or theory.

P(event) =

Trial1 2 3 4 5 6 7 8 9 10

Coin 1 H H H H T H T T H T

Coin 2 T H H T T H T T T H

1) What is the probability that both coins came up the same?

2) What is the probability that both coins come up heads?

3) What is the probability that at least one coins is heads?

4) What is the probability that neither coin is heads?5) If I flip the 2 coins 60 times, how many times would you

expect the result to be 2 heads?

You draw a card from a standard deck of playing cards,

1)What is the probability that you draw a king?

2)What is the probability that you draw a red card?

3)What is the probability that you draw a club ?

4)What is the probability that you draw the jack of hearts?

Possible Outcomes of 2 Number Cubes

1-1 1-2 1-3 1-4 1-5 1-6

2-1 2-2 2-3 2-4 2-5 2-6

3-1 3-2 3-3 3-4 3-5 3-6

4-1 4-2 4-3 4-4 4-5 4-6

5-1 5-2 5-3 5-4 5-5 5-6

6-1 6-2 6-3 6-4 6-5 6-6 36

2 3 4 5 6 7 8 9 10 11 12

6-1

5-1 5-2 5-3

4-1 4-2 4-3 4-4 4-5

3-1 3-2 3-3 3-4 3-5 3-6 4-6

2-1 2-2 2-3 2-4 2-5 2-6 4-5 5-5 6-5

1-1 1-2 1-3 1-4 1-5 1-6 2-6 3-6 4-6 5-6 6-6

2 3 4 5 6 7 8 9 10 11 12 1/36 2/36 3/36 4/36 5/36 6/36 5/36 4/36 3/36 2/36 1/36 1/36 1/18 1/12 1/9 5/36 1/6 5/36 1/9 1/12 1/18 1/36% 2.8 5.6 8.3 11.1 13.9 16.7 13.9 11.1 8.3 5.6 2.8

P(2) P(7) P(10)

10 Rolls

50 Rolls

100 Rolls