Download 11-2 Probability

Find the probability of an event by using
theoretical, experimental, and simulation
methods.
Vocabulary

 An outcome is the result of a single trial
 Sample space is all possible outcomes
 An event is any outcome or group of outcomes.
 The outcomes that match a given event are called
favorable outcomes.
 EX:
Probability

 Tells how likely it is that an event will occur.
 Abbreviated P(event)
 “the probability of an event”
 Ex: P(even)
 That is, the probability of rolling an even number
 Probability ranges from 0 to 1
Theoretical

 When all possible outcomes are equally likely, you
can find the theoretical probability.
 Uses math reasoning
3
6
 EX: P(even) = =
1
2
 Can be written as a fraction, decimal, or percent.
Practice

2
8
 P(distance less than Earth’s) = =
1
4
Complement of an
Event

 All outcomes in the sample space that are NOT in
the event.
 The sum of the probabilities of an event and its
complement is 1.
 P(event) + P(not event) = 1
 So, to find the probability of the complement of an
event: P(not event) = 1 – P(event)
Practice

 Find P(Drink A)
 P(Drink A) =
2
5
 So P(not drink A) = 1 – P(Drink A)
2
5
 P(not drink A) = 1 - =
3
5
Experimental

 Based on data collected from repeated trials.
 Ex: out of 1000 skateboards inspected, 992 were
found to have no defects.
 P(no defects) =
992
1000
= .992 𝑜𝑟 99.2%
Using Experimental
Probability

 Out of 500 households, 197 have dogs. If your town
has 24800 households, how many are likely to have
dogs?
 P(own dog) =
197
500
= 0.394
 Multiply 0.394 ∙ 24800
 9771.2
 Estimate: about 9770 households will own dogs.
Simulation

 If an experiment is unreasonable or difficult to conduct, you
can estimate the experimental probability by using a
simulation.
 Ex: on a multiple choice test, each item has 4 choices. What is
the probability that you will pass the test by guessing at least 6
out of 10 correctly?
 Use a calculator to create the simulation. Let the numbers 1, 2,
3, 4 represent your 4 options and let the number 1 represent a
correct choice.
 Use MATH, move right to the PRB menu and choose randInt(
 Type randInt(1,4,10) to represent choosing digits 1-4 a total of
10 times.
Continued

 You can scroll left and right to view the whole outcome.
 Write down the number of 1’s your calculator generated from
your first trial. This is the number of questions you guessed
correctly.
 Do this 19 more times so that we have 20 trials (taking the test
20 times).
 The goal was to guess at least 6 correct. Count number of times
this occurred.
 Write the experimental probability out of your 20 trials.
Using Combinatorics

 What is the theoretical probability of being dealt exactly two 7’s
in a 5-card hand from a standard 52 card deck?
 We need to know the number of combinations of two 7’s
 4C2 since there are four 7’s and we want 2
 The number of combinations of 3 non-7’s
 48C3 since there are 48 non-7’s and we want 3
 The number of 5 card hands with two 7’s and three non-7’s is
the product 4C2· 48C3
 The sample space is all 5 card hands 52C5
 So the probability is 4C2· 48C3
52C5
 About 4%
Assignment

 Odds p.685 #9-23