Wednesday, February 4 - Probability
Essential questions
-Why do we need to use probability and statistics?
-How are probability and statistics used to solve everyday problems?
- Genetics: In genetics, theoretical probability can be used to calculate the likelihood that offspring will be a certain sex, or that offspring will inherit a certain trait or disease if all outcomes are equally possible. It can also be used to calculate probabilities of traits in larger populations.
- Weather : meteorologists can not exactly predict what the weather will be each week so they use tools and instruments to determine the likelihood of a particular sort of weather. They also examine historical databases to guesstimate temperatures and probable weather patterns. ( USA Today news “Were the predictions we made about climate change 20 years ago accurate? Here’s a look). Have students read and summarize articles.
- Sports Strategies: Athletes and coaches use probability to determine sports strategies for games. (ex- a high school kicker makes 9/15 field goal attempts from over 40 yards. He has a 60% chance of scoring on his next attempt from that distance)
- Insurance options: When choosing a car insurance policy, if 12 out of 100 drivers in your area hit deer in the last year you may want to consider comprehensive insurance rather than just liability. (show probability risk analysis video mass.pbslearningmedia.org/resource/mgbh-math-ee-sprisk/probability-risk-analysis#.Xk_6EIYLRe0.email)
- Games and recreational activities: board games, card games, video games, lottery. The likelihood of getting the cards you’ll need in poker will determine the risk you are willing to take.
- Quality testing: on a day to day basis, we conduct quality tests to ensure that our purchases are correct and we are getting the best results from what we spend.
- Emergency preparedness: with the help of statistics we can predict any natural disaster that may happen and help emergency teams prepare to help those in danger.
- Disease prevention: statistics allows us to know the number of people suffering and who have died from disease as well as the probability of contracting a specific disease.
- Politics: Helps politicians have an idea of their chances of being elected. Helps news channels to predict the winner of the election.
- Financial market: Stock prices are calculated with the help of statistics. Helps individuals to choose investments.
Probability Terms:
Probability: chance of something happening (certain--------> impossible)
Experiment: controlled, repeatable situation that involves chance or probability (ex-rolling a die, flipping a coin, picking a raffle ticket).
Event: set of all possible outcomes for which a probability is assigned (ex- if you were looking to roll a 6 and a 6 came up)
Outcome: one possible result of conducting a probability experiment a single time (possible outcome of rolling a die 1,2,3,4,5,6)
Sample: set of all possible outcomes (if flipping a coin, heads or tails)
Formula for probability: p (A) = number of favorable outcomes
_________________________
Total number of possible outcomes
p=probability
A=event
*a probability can be expressed as a ratio, percent, or a fraction
*a certain outcome or one that is 100% likely to happen has a probability of 1
* an impossible outcome has a probability of 0
Independent vs dependent probability
Independent probability: the probability of one event does not depend on the outcome of the previous event
Dependent probability: outcome of one event depends upon the outcome of the previous event (ex- a bag contains red, orange, green, blue, purple and black marbles. 7 marbles total. You choose 1 red from the bag as the first event. If the red marble is not returned to the bag you now have ⅙ chance of pulling one of the other colors).
How do I solve a probability word problem?
- Identify the experiment and the events
- Find out the number of outcomes of the experiment and every event determined in the 1st step
- Find probability of all events determined in step 1 using values in step 2