Theoretical & experimental
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Probability is the likelihood or chance an event will occur.
Theoretical Probability is the expected probability and can be found with a formula.
Experimental Probability is determined by carrying out an experiment. The more trials you perform, the closer you get to the theoretical probability.
Theoretical Probability is the expected probability and can be found with a formula.
Experimental Probability is determined by carrying out an experiment. The more trials you perform, the closer you get to the theoretical probability.
Compound probability
A Simple Event is the result of a single outcome. For example: Rolling 1 die.
A Compound Event is the probability of two or more simple events. For example: Rolling 2 or more dice, or rolling a die and spinning a spinner.
Independent Events: Events are independent if the outcome of the first event does not effect the probability of the second event.
Key words: "with replacement" Example: rolling 2 dice, or
picking a marble out of a bag, replacing it, and picking a second marble
Dependent Events: Events are dependent if the outcome of the first DOES impact the probability of the second event.
Key words: "without replacement" Example: picking a card out of the deck, & without replacing it, picking another card
picking a marble out of a bag, NOT replacing it, and picking a second marble
RULES for INDEPENDENT EVENTS
Probability of Event #1 OR Event #2 is equal to the Probability of Event #1 ADDED TO the Probability of Event #2.
Probability of Event #1 AND Event #2 is equal to the Probability of Event #1 MULTIPLIED BY the Probability of Event #2.
RULES for DEPENDENT EVENTS
Probability of Event #1 and Event #2 is equal to the Probability of Event #1 multiplied by the Probability of Event #2 AFTER Event #1.
Helpful Hint: If it Depends on the first event, the Denominator is Different.
A Compound Event is the probability of two or more simple events. For example: Rolling 2 or more dice, or rolling a die and spinning a spinner.
Independent Events: Events are independent if the outcome of the first event does not effect the probability of the second event.
Key words: "with replacement" Example: rolling 2 dice, or
picking a marble out of a bag, replacing it, and picking a second marble
Dependent Events: Events are dependent if the outcome of the first DOES impact the probability of the second event.
Key words: "without replacement" Example: picking a card out of the deck, & without replacing it, picking another card
picking a marble out of a bag, NOT replacing it, and picking a second marble
RULES for INDEPENDENT EVENTS
Probability of Event #1 OR Event #2 is equal to the Probability of Event #1 ADDED TO the Probability of Event #2.
Probability of Event #1 AND Event #2 is equal to the Probability of Event #1 MULTIPLIED BY the Probability of Event #2.
RULES for DEPENDENT EVENTS
Probability of Event #1 and Event #2 is equal to the Probability of Event #1 multiplied by the Probability of Event #2 AFTER Event #1.
Helpful Hint: If it Depends on the first event, the Denominator is Different.
Counting outcomes
TREE DIAGRAMS
Drawing a tree diagram is one way to figure out probability when there are multiple choices made. A tree diagram can be used to find the total number of outcomes, by counting the number of "branches" at the end of the tree. It can also be used to find the probability of certain outcomes happening, by writing a fraction of the number of desired outcomes over the total number of possible outcomes.
Drawing a tree diagram is one way to figure out probability when there are multiple choices made. A tree diagram can be used to find the total number of outcomes, by counting the number of "branches" at the end of the tree. It can also be used to find the probability of certain outcomes happening, by writing a fraction of the number of desired outcomes over the total number of possible outcomes.
FUNDAMENTAL COUNTING PRINCIPLE
The Fundamental Counting Principle is a fast way to figure out how many total possible outcome there are for a given situation.
It states that if one event has m possible outcomes and a second independent event has n possible outcomes, then there are m x n total possible outcomes for the two events together.
The Fundamental Counting Principle is a fast way to figure out how many total possible outcome there are for a given situation.
It states that if one event has m possible outcomes and a second independent event has n possible outcomes, then there are m x n total possible outcomes for the two events together.