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10-5, 10-6, 10-7
Probability
EQ: How is the probability of
multiple events calculated?
Probability
Probability: the chance that an event will happen
- a probability of 1 means the event is certain
- a probability of 0 means the event is impossible
Outcome: a result of an experiment
(ex: a bag has 4 marbles = 4 outcomes)
Sample Space: a list of all the possible outcomes
of an experiment
There are 2 ways to count the number of
possible outcomes.
1) make a tree diagram
2) use the Counting Principle
Ex) Three shirts, 4 pairs of pants, and 2 pairs of shoes.
How many outfits are possible?
Try) 3 dice are rolled
Jigsaw
• You will work with a group to become an expert
on a certain topic.
• Then you will work with another group and teach
them your topic
• Everyone will be a student and a teacher today
A = independent events (10-7, p. 727)
B = dependent events (10-7, p. 729)
C = theoretical probability (10-6, p. 720)
D = experimental probability (10-5, p. 713)
Independent & Dependent
Events
EQ: How do you calculate compound
events?
Vocabulary
compound event: an event made up of two or
more simple events
Indepedent Events
independent events: one event has no effect on
the probability of the second event- multiply the
probabilities together
Examples
1) Selecting a marble from a bag then picking
a card from a deck of cards
2) Picking a popsicle stick out of Mrs. Price’s cup of fun,
returning it, then picking another popsicle stick
There are 5 yellow Skittles, 3 purple Skittles, 1 red Skittle, and 1 green Skittle.
Once a Skittle is picked, it is placed back in the bag.
1. Find the P(yellow) then P(purple)
2. Find the P(red) then P(yellow)
Calculating Independent Events
* When calculating the compound probabilities, just multiply
the probability of each event together. Don’t forget to reduce!*
Find the compound probabilities
1. Find the probability of flipping a coin and
getting tails and then rolling a 4 on a number
cube.
P(tails) then P(4)
2. P(red card) then P(odd on a number cube)
3. P(6) then P(6)
Dependent Events
dependent events: one event does have an effect on
the probability of the second event (multiply
the probabilities together)
Examples
1) Selecting a red Skittle and eating it and then
picking out another red Skittle
2) Drawing an Ace out of a deck of cards followed by
drawing a red ten
There are 8 yellow Skittles, 2 purple Skittles, 2 red Skittle, and 3 green Skittle.
Once a Skittle is picked, it is not returned to the bag.
1. Find the P(yellow) then P(green)
2. Find the P(red) then P(purple)
Dependent Events
There are 4 blue socks, 2 red socks, 2 brown socks,
and 4 white socks in a drawer.
1. P(blue) then P(red) (not replaced)
2. P(white) then P(white) (not replaced)
3. P(blue) then P(blue) then P(blue) (not replaced)
Independent or Dependent?
1) Rolling a 2 on a dice then spinning yellow on
a spinner
2) Picking a orange Skittle out of a bag and
eating it, then picking a red Skittle
3) Picking a Jack out of a deck of cards then
selecting a ten out of the deck
Experimental & Theoretical
Probability
EQ: What is the difference between theoretical
& experimental probability?
In experimental probability, the likelihood of an
event is estimated by repeating an experiment
many times and observing what happens (What
actually happens!)
Example: Jane pulled a card out of a deck of 52
cards. Jane would replace the card after each draw.
After 100 trials, she had pulled a red card 58 times
and a black card 42 times.
What is the experimental probability of pulling out
1) a red card?
2) a black card?
Theoretical
Theoretical probability is used to estimate probabilities
when the outcomes are equally likely (what should
happen!)
Example: There are 20 jellybeans in a jar
(5 blue, 5 red, 5 orange, 5 yellow). If I pull 4 jellybeans out,
what should happen?
Try…
If the numbers 0-9 are written on slips of paper and placed
in a hat, what is the theoretical probability of selecting the 4?
When flipping a coin, what is the theoretical probability
of it landing on tails?
***When conducting experiments, the
experimental probability will get closer to the
theoretical probability as you do the
experiment more often!***