10-5, 10-6, 10-7 probability eq: how is the probability of multiple events calculated?
TRANSCRIPT
![Page 1: 10-5, 10-6, 10-7 Probability EQ: How is the probability of multiple events calculated?](https://reader036.vdocuments.us/reader036/viewer/2022081419/56649eb65503460f94bbf7d6/html5/thumbnails/1.jpg)
10-5, 10-6, 10-7Probability
EQ: How is the probability of multiple events calculated?
![Page 2: 10-5, 10-6, 10-7 Probability EQ: How is the probability of multiple events calculated?](https://reader036.vdocuments.us/reader036/viewer/2022081419/56649eb65503460f94bbf7d6/html5/thumbnails/2.jpg)
Probability
Probability: the chance that an event will happen
Outcome: a result of an experiment (ex: a bag has 4 marbles = 4 outcomes)
- a probability of 1 means the event is certain- a probability of 0 means the event is impossible
Sample Space: a list of all the possible outcomes of an experiment
![Page 3: 10-5, 10-6, 10-7 Probability EQ: How is the probability of multiple events calculated?](https://reader036.vdocuments.us/reader036/viewer/2022081419/56649eb65503460f94bbf7d6/html5/thumbnails/3.jpg)
There are 2 ways to count the number of possible outcomes.
1) make a tree diagram2) 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
![Page 4: 10-5, 10-6, 10-7 Probability EQ: How is the probability of multiple events calculated?](https://reader036.vdocuments.us/reader036/viewer/2022081419/56649eb65503460f94bbf7d6/html5/thumbnails/4.jpg)
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)
![Page 5: 10-5, 10-6, 10-7 Probability EQ: How is the probability of multiple events calculated?](https://reader036.vdocuments.us/reader036/viewer/2022081419/56649eb65503460f94bbf7d6/html5/thumbnails/5.jpg)
Independent & Dependent Events
EQ: How do you calculate compound events?
![Page 6: 10-5, 10-6, 10-7 Probability EQ: How is the probability of multiple events calculated?](https://reader036.vdocuments.us/reader036/viewer/2022081419/56649eb65503460f94bbf7d6/html5/thumbnails/6.jpg)
Vocabulary
compound event: an event made up of two or more simple events
![Page 7: 10-5, 10-6, 10-7 Probability EQ: How is the probability of multiple events calculated?](https://reader036.vdocuments.us/reader036/viewer/2022081419/56649eb65503460f94bbf7d6/html5/thumbnails/7.jpg)
Indepedent Eventsindependent events: one event has no effect on
the probability of the second event- multiply the probabilities together
Examples1) Selecting a marble from a bag then picking a card from a deck of cards2) 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)
![Page 8: 10-5, 10-6, 10-7 Probability EQ: How is the probability of multiple events calculated?](https://reader036.vdocuments.us/reader036/viewer/2022081419/56649eb65503460f94bbf7d6/html5/thumbnails/8.jpg)
Calculating Independent Events
Find the compound probabilities1. 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)
* When calculating the compound probabilities, just multiply the probability of each event together. Don’t forget to reduce!*
![Page 9: 10-5, 10-6, 10-7 Probability EQ: How is the probability of multiple events calculated?](https://reader036.vdocuments.us/reader036/viewer/2022081419/56649eb65503460f94bbf7d6/html5/thumbnails/9.jpg)
Dependent Events
Examples1) Selecting a red Skittle and eating it and then picking out another red Skittle2) Drawing an Ace out of a deck of cards followed bydrawing 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: one event does have an effect on the probability of the second event (multiply the probabilities together)
![Page 10: 10-5, 10-6, 10-7 Probability EQ: How is the probability of multiple events calculated?](https://reader036.vdocuments.us/reader036/viewer/2022081419/56649eb65503460f94bbf7d6/html5/thumbnails/10.jpg)
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)
![Page 11: 10-5, 10-6, 10-7 Probability EQ: How is the probability of multiple events calculated?](https://reader036.vdocuments.us/reader036/viewer/2022081419/56649eb65503460f94bbf7d6/html5/thumbnails/11.jpg)
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
![Page 12: 10-5, 10-6, 10-7 Probability EQ: How is the probability of multiple events calculated?](https://reader036.vdocuments.us/reader036/viewer/2022081419/56649eb65503460f94bbf7d6/html5/thumbnails/12.jpg)
Experimental & Theoretical Probability
EQ: What is the difference between theoretical & experimental probability?
![Page 13: 10-5, 10-6, 10-7 Probability EQ: How is the probability of multiple events calculated?](https://reader036.vdocuments.us/reader036/viewer/2022081419/56649eb65503460f94bbf7d6/html5/thumbnails/13.jpg)
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?
![Page 14: 10-5, 10-6, 10-7 Probability EQ: How is the probability of multiple events calculated?](https://reader036.vdocuments.us/reader036/viewer/2022081419/56649eb65503460f94bbf7d6/html5/thumbnails/14.jpg)
TheoreticalTheoretical probability is used to estimate probabilities when the outcomes
are equally likely (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?
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?
![Page 15: 10-5, 10-6, 10-7 Probability EQ: How is the probability of multiple events calculated?](https://reader036.vdocuments.us/reader036/viewer/2022081419/56649eb65503460f94bbf7d6/html5/thumbnails/15.jpg)
***When conducting experiments, theexperimental probability will get closer to the
theoretical probability as you do theexperiment more often!***