April 03, 2013

Theoretical Probability

Objective:

Learn to estimate probability using theoretical methods.

The probability of an event is a number from 0 to 1 (or 0% to 100%) that tells us how likely the event is to happen.

April 03, 2013

April 03, 2013

Theoretical Probability - is used to estimate probabilities by making certain assumptions about an experiment.

Outcome - result of an experiment.

An experiment is an activity in which results are observed. Each observation is called a trial, and each result is called an outcome.

Total number of possible outcomes

April 03, 2013

Suppose there are n equally likely outcomes in an experiment.

• The probability of EACH individual outcome is 1/n.

• The probability of an event is number of outcomes in an event

n

Equally Likely - All of the outcomes have the same probability. Also, the sum of all the probabilities must add up to 1.

Ex: Are the results of rolling a dice equally likely?

• Find the probability of rolling a 4.

• Find the probability of rolling a 6.

April 03, 2013

Independent Event - the occurrence of one event does NOT affect the probability of the other.

Ex: A coin landing on heads and then landing on tails on another toss.

Compound event is made up of two or more separate events.To find the probability of compound events, we first need to classify them as independent or dependent events.

Dependent Event - the occurrence of one event DOES affect the probability of the other.

Ex: Drawing a 6 from a deck of cards and then drawing a 7.

April 03, 2013

There are 2 red cubes and 2 white cubes in a cup. In each situation below, the first cube drawn is put back in the cup before the second draw.

a. If you pull out a red cube first, what is the theoretical probability of getting a white cube on the second draw? _________

b. If you pull out a white cube on the first draw, what is the theoretical probability of getting a white cube on the second draw? _________

c. In the above situations, are the events independent or dependent? ______________________

d. What would cause the answer to “c” to be different? ______________________

April 03, 2013

In a bag with 20 marbles, 4 marbles are blue.

a. One marble is drawn from the bag. What is the probability that it is a blue marble? __________ What is the probability that it is not a blue marble? ___________

b. Suppose a blue marble is drawn on the first draw and it is not replaced. What is the probability of drawing a blue marble on the second draw? ______________

c. Suppose another color (not blue) is drawn on the first draw and is not replaced. What is the probability of drawing a blue marble on the second draw? ___________

d. Is drawing a blue marble on the second draw dependent or independent of the first draw?

April 03, 2013

Impossible Event – A probability of 0 means the event is impossible.

Certain Event – A probability of 1 means the event is certain, or has to happen.

April 03, 2013

An experiment consists of rolling two fair number cubes. Find the probability of each event.

a. Probability of rolling a sum of 4

P(sum of 4) = _________________

b. Probability of rolling a sum of 1

P(sum of 1) = _________________

c. Probability of rolling at least one 5

P(at least one 5) = _____________

d. Probability of rolling a 8

P(8) = ______________________

April 03, 2013

Determine if the outcomes of the events described are equally likely.

a. Rolling an even number on a number cube with sides numbered 1-6 and rolling an odd number on the same cube ___________________

P(even number) = P(odd number) =

b. Rolling a number less than 2 on a number cube with sides numbered 1-6 and rolling a number greater than 3 on the same cube __________________

P(<2) = P(>3) =

c. Spinning a 1 on this spinner and spinning a 3 on this spinner ___________________

April 03, 2013

Stephany has 2 dimes and 3 nickels. How many pennies should be added so that the probability of drawing a nickel is 3/7?

Let x equal the number of pennies.

April 03, 2013

What color should you shade the blank region so that the probability of the spinner landing on that color is 1/2?

RR

RB

B

YG

April 03, 2013