PROBABILITY Probability a number that describes how likely

PROBABILITY

Probability – a number that describes how likely an event is to occur.

Probability can be expressed as: - a fraction 1/2 -a decimal . 9 - a percent 50%

First, this does assume all sides are equally likely to come up. Equally likely- all outcomes have the same chance.

Terminology At random: all outcomes have a equal chance of occurring Favorable outcome: the outcome you want to occur. Possible outcome: all the possible results of an experiment sample space: the set of all possible outcomes ( {1, 2, 3, 4, 5, 6} ) With replacement- returning the outcome to the sample space Without replacement- not restoring an outcome

P ( ) = Probability of an event Example: P (6) means the probability of rolling a six

An event that has probability 1 must always happen. It is called a sure or certain event. experiment: Toss coin event: heads or tails When you toss a coin, you must get either a heads or a tail. An event that has probability 0 will never happen. It is called an impossible event. experiment: Roll die event: roll 7 When you roll a six-sided die, you cannot get a 7.

What is probability? Probability discusses the likelihood or chance of something happening. For instance, -- the probability of it raining tomorrow -- the probability of rolling a 4 on a six-sided die -- the probability of being struck by lightning -- the probability of pulling an Ace out of a deck of cards -- the probability of meeting your spouse on a blind date

Independent events Two events are independent if the occurrence of one does not affect the occurrence of the other. The events of rolling a “ 4” on a die and spinning red are independent because the occurrence of the 4 on the die does not affect the probability that I will get an red also.

Dependent Events Two events are dependent if the occurrence of one does affect the occurrence of the other. The events of choosing a King from a deck of cards and then a Queen are dependent because the occurrence of the second is dependent on the first.

Theoretical vs. Experimental Probability Theoretical Probability: - The probability we find on paper. - It is how a probability of an event “should” happen. Experimental Probability: - Experimental probability refers to the probability of an event occurring when an experiment was conducted.

Theoretical vs. Experimental Probability Theoretical Probability: number of favorable outcomes Theoretical Probability= number of possible outcomes

Theoretical vs. Experimental Probability: number of event occurrences Experimental Probability= Total number of trials

Theoretical vs. Experimental Probability Example 1: Roll a dice. What is theoretical probability of rolling a 4? # favorable outcomes # possible outcomes 1 6 The probability of rolling a 4 is 1 out of 6

Theoretical vs. Experimental Probability Example 1 Continued: Roll a dice. What is the experimental probability of rolling a 4? # event occurrences Total # of trials

Theoretical vs. Experimental Probability Example 2: Coins. What is theoretical probability of flipping a tail? # favorable outcomes # possible outcomes 1 2 The probability of spinning green is 1 out of 2 or. 5 or 50%

Theoretical vs. Experimental Probability Example 2 Continued: Coins. What is the experimental probability of flipping a tail? # favorable outcomes # possible outcomes