probability calculates the likelihood an event will occur must lie between 0 and 1
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Probability Calculates the likelihood an event will occur Must lie between 0 and 1 “ 0 ” implies that the event will not occur “ 1 ” implies that the event will definitely occur . Probability of an Event: P(A). Sample Space: The set of all possible outcomes of an experiment - PowerPoint PPT PresentationTRANSCRIPT
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Probability Calculates the likelihood an event will occur
• Must lie between 0 and 1• “0” implies that the event will not occur• “1” implies that the event will definitely occur
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Probability of an Event: P(A)
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Sample Space: The set of all possible outcomes of an experiment
Example: You are rolling two dice, what is the sample space?
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Sample Space: The set of all possible outcomes of an experiment
Example: picking a card, what is the sample space?
• 52 cards• 13 cards in each suits• 12 face cards• 4 suits:
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6.5
Example• What is the probability of each of the events
occurring when rolling two dice?
1) P(they add up to 2) = ?• P(2) = 1/36
2) P(6) = ?• P(6) = 5/36
3) P(10) = ?• P(10) = 3/36
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Independent Events: the occurrence of one does not affect the probability of the other
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Multiplication Rule Finding the probability of more than one event.
The word “AND” is always used when describing the situation.
1) P(rolling a 4 and then a 2) = 1/6 *1/6 = 2.8%2) P(rolling three odd numbers in a row) = 3/6*3/6*3/6=12.5%
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Multiplication Rule for Independent Events
P(A and B) = P(A) * P(B)
Example: What is the probability of rolling five 6’s in a row on a six sided die.
P(6&6&6&6&6) = (1/6) (1/6) (1/6) (1/6) (1/6)= 0.0001
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P(A and B) = P(A) * P(B)
Example:
There are 11 marbles in a bag.
2 yellow, 5 pink, 4 green
You pull out one marble and put it back in the bag and then pull out another marble. What is the probability of picking pink twice in a row
P(pink and pink) = (5/11)*(5/11) = 25/121 = 21%
Multiplication Rule for Independent Events
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What is the probability of getting heads on a coin flip AND picking a brown ball out of a bag?
P(heads and blue ball) Option #1: Multiply the probability of heads and brown ball: 1/3*1/2
Option #2:a) find the size of
the sample space
b) count the outcome of interest
c) Use results from a and b to find the probability
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Compliment of an Event
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If A is an event within the sample space S of an activity or experiment, the complement of A (denoted A') consists of all outcomes in S that are not in A.
The complement of A is everything else in the problem that is NOT in A.
Complement:P(A') = 1 - P(A)