MATH 109 Lecture 5: 5.2 Stats: Finding Theoretical Probabilities, Mutually Exclusive Events

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15 Jun 2018
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5.2
Finding Theoretical Probabilities
- Probability are always numbers between 0 and 1.
- 0 means that the event never
happens.
- 1 means that the event always
happens.
- 1- means that the event will not
happen.
Complement- “not event”
Equally Likely Outcomes- in some situations, all of the possible outcomes of a random
experiment occur with the same frequency.
-Example: when you flip a coin, heads and tails are equally likely; when you roll a die,
1,2,3,4,5, and 6 are all equally likely.
- When dealing with equally likely outcomes, it is sometimes helpful to list all of the
possible outcome.
Sample space- a list that contains all possible (and equally likely) outcomes.
- Represent the sample space with the letter s.
Event- any collection of outcomes in the sample space.
-Example: the sample space, s
, for rolling a die is the numbers, 1,2,3,4,5, and 6. The
event “get an even number” consist of the even outcomes in the sample space, s:
2,4,
and 6.
- Events are represented by uppercase letters: A,B,C, and so on …
Rule 1: A probability is always a number from 0 to 1 or (0% to 100%) inclusive (which means 0
and 1 are allowed). It may be expressed as a fraction, a decimal, or a percent.
0 P(A) 1
Rule 2: The probability that an event will not occur is 1 minus the probability that the event will
occur.
P(A does not occur) = 1 - P(A does occur)
P(Ac) = 1 - P(A)
The symbol Ac is used to represent the complement of A.
Rule 3: Probability of A = P(A) = Number of outcomes
Number of all possible outcomes
This is true only for equally likely outcomes.
Ex 12: 10 Dice in a Bowl
Bowl contains:
- 5 red dice (5/10 or 50%)
- 3 green dice (3/10 or 30%)
- 2 white dice (2/10 or 20%)
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Document Summary

Probability are always numbers between 0 and 1. 1- means that the event will not happen. Equally likely outcomes- in some situations, all of the possible outcomes of a random experiment occur with the same frequency. Example : when you flip a coin, heads and tails are equally likely; when you roll a die, When dealing with equally likely outcomes, it is sometimes helpful to list all of the. 1,2,3,4,5, and 6 are all equally likely. possible outcome. Sample space - a list that contains all possible (and equally likely) outcomes. Event- any collection of outcomes in the sample space. Represent the sample space with the letter s. Example : the sample space, s , for rolling a die is the numbers, 1,2,3,4,5, and 6. The event get an even number consist of the even outcomes in the sample space, s: 2,4, and 6. Events are represented by uppercase letters: a,b,c, and so on .

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