Probability
Big ideas
Probabilities are measured with numbers between 0 and 1, or percents between 0 and 100.
If the probability of something happening is measured by the number P, then the probability of it not happening is 1-P
Figuring out the probability of something happening is a matter of making a ratio of (ways it can happen)/(equally likely things that can happen)
If you have a big enough pool of trials (by having multiple people do something, or by doing something a large amount of times), even very unlikely things can happen
Probability is best for figuring out what will happen over the long term. Probability may not help you if you are deciding what to do once, but it can really pay off if you are doing something a lot of times.
Figuring out the probability for what can happen with two dice or two spinners is something you can do by using a grid.
The probability of two things both happening is less than the probability of just one of the things happening, and you get that probability for both by multiplying the probabilities of them happening separately. Choosing two things out of a group is easiest to analyze by multiplying.
Study questions
1. I have two 10-sided dice, numbered 1-10. If I toss both of them, what is the probability that I will get
2. I have two funny spotted 6-sided dice. Die A has the numbers: 1, 1, 3, 3, 5, 6 and die B has the numbers 2, 2, 2, 4, 4, 4
3. If I have the pair of spinners below, what is the probability, when I spin both, that the sum will be 3? What is the probability of getting a sum of 4?
4. If I have a bag with 5 red and 3 blue marbles, and I pick two out (one and then the other,without replacing the first)
5. Each of the spinners below costs $4.00 to play. If your friend is planning to play 100 times, which spinner would you reccommend that he use? (explain why)
6. Mystico the astrologer for a well read newspaper predicted that if you are
an Aquarius, you will soon hear from a friend you have not spoken to in a very
long time. For the purposes of this assignment, assume that "a very long
time" means more than 10 years, and that "soon" means this week.
Assume also that a large number of people read the column every day.
A. Is it likely or unlikely that this will happen to every Aquarius who is over
age 15? (Explain)
B. Is it likely or unlikely that this will happen to at least one Aquarius who reads Mystico’s column? (Explain)
7. The weatherman says that there is a 40% chance of rain tomorrow. What is the probability that it will not rain tomorrow?