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Algebra 1
1.6 ‐ Probability
A. Probability
Probability ‐ the probability of an event occurring, or P(event), tells how •
likely it will occur.
Probabilies of events are expressed as numbers ranging from 0 to 1, or •
0% chance of something occurring to 100% chance of something occurring. The closer the probability of a given event occurring is to 0, the less •
likely it will occur.
The closer the probability of a given event occurring is to 1, the more •
likely it will occur.
The Outcome is the result of a single trial
•
The Event is any outcome or group of outcomes
•
The Sample Space is all possible outcomes
•
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B. Theoretical Probability:
Experiment ‐ an occurrence in which the outcome is uncertain (flipping •
a coin)
Theoretical Probability ‐ the probability that applies to situations in •
which the sample space contains equally likely outcomes, all of which are known. NOTE: you can write the probability of an event as a fraction, a decimal, •
or a percent
Computing Theoretical Probability:
If an event E has n(E) equally likely outcomes and its sample space S has n(S) equally likely outcomes, the theoretical probability of event E, P(E) is
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C. Probability of an event not occurring
This is also called the complement of an event; the probability that an •
event won’t occur.
We know that if the probability of an event occurring is 1, then there •
is a 100% chance it will occur.
In determining the probability of an event not occurring, we can •
simply take the probability that the event will occur and subtract it from 1. For example, let's say we roll a die. What is the probability of rolling a •
6? What is the probability of not rolling a 6?
The Probability of an Event Not Occurring:
The probability than an event E will not occur is given as Oct 6­9:40 AM
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D. Use the spinner at the right to find the theoretical probability of landing on certain sections. 2. P(7 or 8)
1. P(blue)
1
2
8
3
7
4
6 5
3. P(not green) 4. P(red or yellow)
5. P(even number)
6. P(not even)
7. P(purple)
8. P(red, green, blue, yellow)
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E. More theoretical probability examples. A 6‐sided die is rolled. Find the probability of rolling
2. A number less than 5 1. not 3
3. A number greater than 4
4. An odd number
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F. Experimental Probability
Experimental Probability ‐ probability based on data collected from •
repeated trials Computing Experimental Probability, P(event) = Oct 6­11:47 AM
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G. Use experimental probability to answer the following.
1. Quality control inspected 500 belts at random. They found no defects in 485 belts. What is the probability that a belt selected at random will pass quality control?
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D. Target Games. Assume a dart is thrown at random find the H.
probability that it will land in the shaded region
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7. Example 3 page 583
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12 in
12 in
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1.6 HW. p. 42 #s 1, 2, 6 ‐ 20 all
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