Probability
More Probability
Theoretical vs Experimental Probability
Here Come the Outcomes
Closer to Zero or Closer to One
100
List the terms of the Probability Scale in order from 0 to 1.
Impossible, Unlikely, Equally Likely, Likely, Certain.
100
What principle would I use to determine the number of outcomes, using multiplication?
Counting Principle
100
For 20 trials your Experimental Probability for blue is 8/20.
What is the Theoretical Probability you will choose Blue after 100 trials?
P(Blue) = 40/100
100
You randomly choose a letter from the word
OUTCOMES
Give the SAMPLE SPACE
O, U, T, C, M, E, S
100
You have a jar with 45 Plain M&Ms and 55 Peanut M&Ms. You choose a Plain M&M.
Is P(Plain) closer to Zero or Closer to One?
P(Plain) = 45/100
45/100 is less than 1/2, so closer to 0.
200
What is Relative Frequency?
The number of outcomes for an experiment.
200
3 Shirts, 2 pants, 6 shoes.
How many different outcomes would I have?
36
200
You have twelve pairs of socks in your sock drawer. 3 pairs are blue, 4 pairs are black, 5 pairs are striped.
Is P(striped) = 5/12
the Experimental Probability or the Theoretical Probability
Theoretical Probability
200
Homer can order Coffee, or Hot Cocoa, he can have a breakfast sandwich or Oatmeal, he can choose a donut with jelly, sprinkles, or glaze. How many different combinations of drink, breakfast, and donut can Homer choose from?
2 drinks, 2 breakfasts, 3 donuts
2 x 2 x 3 =12 different combinations
200
You have twelve pairs of socks in your sock drawer. 3 pairs are blue, 4 pairs are black, 5 pairs are striped.
You reach in and pull out a black pair of socks.
Is P(black) closer to Zero or Closer to One?
Closer to Zero
300
How can relative frequency get closer to the theoretical probability?
Do more trials (or experiments).
300
Nickel (Heads or Tails) Die ( 1-4)
State three possible outcomes
H1 T1
H2 T2
H3 T3
H4 T4
300
You have 30 marbles in a box. After drawing a random marble for 10 trials, you have
P (orange marble) = 6/10
Is P (orange marble) = 6/10 Experimental Probability or Theoretical Probability
Experimental Probability
300
You spin this spinner twice, use the counting principle to determine the number of possible outcomes.
First Spin - 3 outomes
Second Spin - 3 Outcomes
3 x 3 = 9 -- Nine Possible outcomes
300
You have the days of the week written on strips of paper and placed in a bag. You choose a day at random.
Is P(the day has an A in it) closer to Zero or Closer to One?
Every day has an A in it! So, closer to 1.
400
If I had 10 cubes, 4 green, 5 orange, 1 yellow.
Using Theoretical Probability, Which color would have a higher percentage of being picked out of a bag?
Orange, 5/10 = 1/2 = .50 = 50%
400
State two ways to organize data
Sample Space
Tree Diagram
400
You have 30 marbles in a box. After drawing a random marble for 10 trials, you have
P (orange marble) = 6/10
What is the Theoretical Probability P (orange marble) for 60 trials?
P (orange marble) = 6/10 = 36/60
400
You spin this spinner twice, give the Sample Space
BB RR YB
BR RY YR
BY RB YY
400
You have a bag with 12 black, 8 white and 30 gray marbles. You reach in the bag and pull out a gray marble.
Is P(Gray) closer to Zero or Closer to One?
30/50 is greater than 1/2, so, closer to 1.
500
Fill in the blank: The more trials you do, the ___________ you will get to the Theoretical Probability.
A. Nearer
B. More Equal
C. Closer
D. All of the Above
500
Experimental Theory resulted in:
Yellow 3/10
If I did 100 trials, what would be the Theoretical Probability?
3/10 = x/100 Solve for "x" :
30
500
You choose 7 red jelly beans out of 10 trials. If you repeated this experiment for 100 trials, what is:
P(red jelly bean) = ?
P (red jelly bean) 7/10 = 70/100
500
You flip a coin and roll a number cube contains the numbers, 1,2,3,4,5,6.
Calculate the Probability of (tails, odd)
P(tails) = 1/2
P(Odd) = 3/6 = 1/2
P(tails, odd) = 1/2 x 1/2 = 1/4
500
There are four vowels in the name VIGLIOTTI
Of the four vowels you choose the letter I.
Is P (Choose the letter I) closer to Zero or Closer to One?
When choosing only among the vowels
P (I) = 3/4
3/4 > 1/2, therefore closer to 1.