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Probability Cheat Sheet
Defined!
Probability: predicts how likely or unlikely
something is to occur
Probability measures will fall between 0 and 1 as a
fraction or a decimal.
Probability can be written as a fraction, a decimal,
or a percentage!
2/5 = 0.4 = 40%
Likely is more than ½
Unlikely is less than ½.
0 = unlikely
½ = as likely
as not
1 = certain
Experimental Probability: “Do something” about it.
Theoretical Probability: “Think about it.”
Any probability answers will come from recorded
data or information from an experiment.
Any probability answers will come from the
possible and expected outcomes.
Probability:
Simple Probability: One event occurs at one time.
P(event) = number of times the event occurs
number of possible outcomes
Find the probability as listed to the left.
Compound Probability: 2 or more events happen
in a row or together.
Sample Space – a list of all possible outcomes
Ex: For a die: {1,2,3,4,5,6}
Find it: you find each individual probability and
MULTIPLY the fractions
For the word CANADA: {C,A,N,D}
Independent Events: The outcome of an event does
not affect any other outcome
Ex: 3 coin flips in a row: Tree Diagram
Dependent Events: The outcome of one trial will
affect the outcome of future trials.
H
H
T
T
H T
H T H T H T H T
Special Situations:
Special Situations:
When rolling a single die: P(rolling a 1 or 6) “or”
means to combine 1 and 6 into one successful
group. ADD the total numbers of 1’s and 6’s.
When doing any successive trials (compound
probability) look for the word “Then” as a
keyword.
QUESTION
ANSWER
Example 1: You have a grocery bag with 3 green
peppers, 2 bananas, 1 carrot, 4 cucumbers.
A: It is more likely (7/10), but not certain (1) that
you will pull a green item from the bag. The
fraction 7/10 = 0.7, which is greater than ½ (0.5).
Example 2: You have 3 choices of snack after
school. The probability of choosing a fruit is 3/12,
probability of a vegetable is 2/6, what is the
probability of getting something sugary?
A: The sum of all three must equal 1. So 3/12 +
4/12 = 7/12. That leaves 5/12 as the remainder to
reach 1. So the probability of something sugary is
5/12
A: P(boy) = ¾ also equal to 0.75
P(girl) = ¼
also equal to 0.25
Example 3: Is the probability
of choosing a boy closer to 0 or 1? A girl?
The probability of a boy at ¾ is closer to 1. The
probability of a girl at ¼ is closer to 0.
Example 4: You roll a single die 42 times. Rolling
a 4 is considered successful. You roll a 4 16 times.
What is the relative frequency of getting a 4?
A: The relative frequency is how often you have a
successful outcome. So 16/42 = 0.3809 = 38%
The theoretical success rate is 1/6 = 0.16666 = 17%
In this case you were overly successful when
comparing your experiment to theoretical. This is
due to a small set of trials. Increasing the number
of trials will show your experimental results to get
closer and closer to the theoretical probability.
Example 5: In a bag of scrabble letters there are
42 vowels and 58 consonants in the bag. After
1000 pulls, how many times would a vowel be
selected? After 10,000 pulls?
Example 6: In a bag of 25 jelly beans, there are 6
green, 4 yellow, 8 orange, 3 red, and 4 white
beans. What is the probability of pulling a red
bean, eating it and then pulling white bean?
A: If the P(vowel) = 42/100 then
42 (x10) = 420
100 (x10) 1000
OR 42 (x100) = 4200
100 (x100) 10,000
So 420 vowels would be pulled in 1000 tries and
4200 vowels would be pulled in 10,000 tries.
A: The P(red) = 3/25. After eating the jelly bean
there are only 24 beans remaining so the
P(white) = 4/24. MULTIPLY then and find that
3 x 4 = 12 This can be simplified to 1.
25
24 600
50
Example 7: If I chose the red jelly bean above,
didn’t like and replaced it, then chose a second
time, what is the P(red, white)
A: P(red) = 8/75. If I replace it, the 75 remains
constant. So P(white) = 14/75. MULTIPLY them
3 x 4 = 12
25 25 625
Example 8: How many ways can three dogs enter
the vet’s office (Rover, Mack, and Fido)
A: An organized list or tree diagram could help list
the 6 possible outcomes:
RMF
MRF
FRM
RFM
MFR
FMR