Download Chapter 10.6 Theoretical Probability

Chapter 10.6 theoretical probabilty.notebook
April 27, 2017
Bellwork:
Homework Questions???
1) Solve the system by graphing (hint: graph on same coordinate plane)
2) An experiment consists of spinning a spinner 8 times. The spinner lands on red 4 times, yellow 3 times, and green once. Find the experimental probability of each event.
a. the spinner lands on red
b. the spinner lands on yellow
c. The spinner does not land on green
d. spinner lands on black
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Yesterday we discussed experimental probability, today we will look at theoretical probability.
Equally Likely: the outcomes in sample space have the same chance of a occurring.
Chapter 10.6 Theoretical Probability
Determine the theoretical probability of an event. Convert between probabilities and odds.
Equally likely outcomes
Not equally likely outcomes
There is the same chance that the spinner will land on any of the colors.
There is a greater chance that the spinner will land on purple than on any other color.
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Theoretical Probability: the ratio of the number of ways the event can occur to the total number of equally likely outcomes.
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1) An experiment consists of rolling a six­sided dice. Find the theoretical probability of each outcome.
a. rolling a 5
b. rolling an odd number
c. rolling a number less than 3
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Chapter 10.6 theoretical probabilty.notebook
April 27, 2017
We often write the probability of an event as P(event).
2) An experiment consists of spinning the shown spinner.
a. landing on red P(heads) would mean the probability that heads will be the outcome. P(heads)
b. not landing on yellow
c. landing on purple or blue?
P(tails)
P(heads) + P(tails)
Experimental Probability
Theoretical Probability
The sum of the probability of heads and the probability of tails is 1, or 100%. It is certain that one of the two outcomes will always occur.
P(event happening) + P(event not happening) = 1
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Complement: of an event is all the outcomes in the sample space that are not included in the event. The sum of the probabilities of an event and its complement is 1 or 100%.
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3) Find probability by using the complement.
a. The weather forecaster predicts a 30% chance of rain. What is the probability the it will not rain?
P(event) + P(complement of event) = 1
Example:
A box contains only red, black, and white blocks. The probability of choosing a red block is 1/4, the probability of choosing a black block is 1/2. What is the probability of choosing a white block?
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Odds: express the likelihood by comparing the number of ways an event can happen to the number of ways an event can fail to happen. (often written as a ratio a:b) Odds in favor of an event: likelihood that the event will occur.
Odds against an event: likelihood that the event will not occur. b. A jar has green, blue, purple, and white marbles. The probability of choosing a green marble is 0.2, the probability of choosing blue 0.3, and the probability of choosing purple is 0.1. What is the probability of choosing white?
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4) Converting between odds and probabilities a. The probability of rolling a 2 on a number cube is 1/6. What are the odds of rolling a 2. b. The odds in favor of winning a contest are 1:9. What is the probability of winning the contest?
Odds in Favor of an Event with Equally Likely Outcomes:
c. The odds against a spinner landing on red are 2:3. What is the probability of the spinner landing on red?
Odds Against an Event with Equally Likely Outcomes:
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Chapter 10.6 theoretical probabilty.notebook
April 27, 2017
Homework
P. 737­739 #1­27 (odds), 30, 32
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