 # 10.1 & 10.2 Probability & Permutations. WARM UP:

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10.1 & 10.2 Probability & Permutations

WARM UP:

TermDefinitionExample Trial Experiment Sample Space Event A systematic opportunity for an event to occur One or more trials rolling a die rolling a die ten times The set of all possible outcomes1, 2, 3, 4, 5, 6 An individual outcome or Any specified combination of outcomes rolling a 3 rolling a 3 or rolling a 5

Outcomes are random if all Probability is expressed as a number between 0 and 1. It can be written as a An impossible event An event that must occur has a The sum of the probabilities of all outcomes in the sample space is fraction, decimal, or percent. possible outcomes are equally likely. has a probability of 0. probability of 1. 1.

Approximated by performing trials and recording the ratio of Experimental Probability: the number of occurrences of the event to the number of trials.

1a. Find the probability of randomly selecting a blue marble in one draw from a bag containing 2 red marbles, 4 blue marbles, and 3 yellow marbles. The event is one blue marble. Because there are 4 blue marbles, the number of outcomes in the event is 4. The sample space is the set of all marbles, so the total number of outcomes in the sample space is 2 + 4 + 3, or 9.

The Fundamental Counting Principle If there are m ways that one event can occur and n ways that another event can occur, then there are m x n ways that both events can occur.

Probability versus Odds If one day of the week is randomly chosen, the probability that the chosen day will be Tuesday is: If one day of the week is randomly chosen, the odds that Wednesday will be chosen are: 1 to 6 Odds, expressed a ratio, compare the chance of an event happening to the chance of it NOT happening.

Ex 6. There are 1200 students at South Penn High School, 760 of whom are boys. What are the odds of a girl being randomly chosen to win concert tickets? There are 1200-760, or 440 girls, so the odds of a girl being chosen can be found by comparing the chances of a girl being chosen to the chances that a girl is NOT chosen. 440 to 760 Or 11 to 19

10.2 - Permutations