IB  SL  2  -­‐‑  Lesson  12.1:  Some  Definitions     Unit  12:  Probability  

Big Picture We have finished Statistics… a bit… we will continue to work with Normal Distribution but we now move into our last unit of Probability.

Context of this Lessons

Building some Definitions for our Probability Unit.

 

To Do Today!

-­‐ Task 0: Warm Up

-­‐ Task 1: Investigation/Discussion

-­‐ Task 2: Chances Are…

-­‐ Task 3: Theoretical Probability

-­‐ Task 4: Experimental Probability

- Task 5: Practice

Task 0: Warm Up

IB  SL  2  -­‐‑  Lesson  12.1:  Some  Definitions     Unit  12:  Probability  

Task 1: Investigation into Dice and Probability

Roll of a Six on Four Throws of 1D6

Double Six on 24 Throws of 2D6

Given this experiment… which was more likely? What is the expected outcome of Discuss… Actual Probability?

IB  SL  2  -­‐‑  Lesson  12.1:  Some  Definitions     Unit  12:  Probability  

Task 2: Chances are you’ve done this before… Find the “probability” of each of the below events… please put your number as a fraction and a decimal.

D6 D20 Coin 52 Cards # of Dice: 1 Event A: Roll a 3 P(A) =

# of Dice: 1 Event B: Roll a 20 P(B) =

# of Coins: 1 Event C: Heads P(C) =

# of Trials: 1 Event D: Ace P(D) =

# Dice: 1 Event A: Roll Even P(A) =

# of Dice: 1 Event B: Roll a Prime P(B) =

# of Coins: 1 Event C: Tails P(C) =

# of Trials: 1 Event D: Spade P(D) =

# Dice: 1 Event A: Roll a 2 - 5 P(A) =

# of Dice: 1 Event B: Multiple of 4 P(B) =

# of Trials: 1 Event D: Face Card P(D) =

# Dice: 1 Event A: Roll a 1 - 5 P(A) =

# of Dice: 1 Event B: 2 - 18 P(B) =

# of Trials: 1 Event D: # Card P(D) =

# Dice: 1 Event A: Roll a 7 P(A) =

# Dice: 1 Event B: Roll a 21 P(B) =

# of Trials: 1 Event D: Not an Ace of Spades P(D) =

Task 3:

IB  SL  2  -­‐‑  Lesson  12.1:  Some  Definitions     Unit  12:  Probability  

Task 3: Theoretical Probability With any Event A, there is all the possible outcomes of A and all the possible outcomes of the Sample Space U that A is apart of… Take 1D6. The Sample space is all the possible outcomes of the Die… 1, 2, 3, 4, 5, 6 n(U) = 6. Event A: Roll an Even {2, 4, 6} = n(A) = 3

Sample Space U: 1D6 {1,2,3,4,5,6} n(U) = 6

Probability of Event A P(A) = n(A)/n(U) =3/6 = 0.5

IB  SL  2  -­‐‑  Lesson  12.1:  Some  Definitions     Unit  12:  Probability  

Task 4: Experimental Probability One of the important aspects of Theoretical Probability is that each outcome has an equal chance of happening. This is not always the case and we must use real world data to get a ball park figure of outcomes.

Ok, let us assume we are managers of a factory and produces widgets. Now, this factory will produce some working widgets and some faulty widgets. How might we get a feel for the % of Faulty widgets we will produce?

If we test the first widget and it is faulty… do we assume 100% will be faulty? If we test the first two and one is faulty and the second is not do we assume 50% failure? How do we get a better prediction?