1. Chapter 5 Review MDM 4U
Gary Greer

2. 5.1 Probability Distributions and Expected Value
determine the probability distributions for discrete random variables
determine the expected value of a discrete random variable
ex: what is the probability distribution for results of rolling an 8 sided die?
Roll 1 2 3 4 5 6 7 8
Prob. ⅛

3. 5.1 Probability Distributions and Expected Value
ex: what is the expected value for rolling an 8 sided die?
ans: 1(⅛) + 2(⅛) + 3(⅛) + 4(⅛) + 5(⅛) + 6(⅛) + 7(⅛) + 8(⅛) = 4.5

4. 5.2 Pascal’s Triangle and the Binomial Theorem
determine the number of paths using Pascal’s Triangle
use the binomial theorem to expand binomials
find a particular term in a binomial expansion
formulas are present on exam

5. 5.2 Pascal’s Triangle and the Binomial Theorem
ex: find the number of paths through a grid where you can only move up or right
ans: C(7,4) or C(7,3)

6. 5.2 Pascal’s Triangle and the Binomial Theorem
ex: expand (3 + x)³
ans:

7. 5.2 Pascal’s Triangle and the Binomial Theorem
ex: find the term in the following with d²

8. 5.3 Binomial Distributions
recognize a binomial experiment situation
successive events (trials)
same probability
two possible outcomes
calculate probabilities for these situations
ex: roll an 8 sided die 4 times. what is the probability that the first will be a 1 and the rest will be something other than a 1?
(⅛)(⅞)(⅞)(⅞)

9. 5.3 Binomial Distributions
ex: A family decides to buy 5 dogs. If the chances of picking a male and female are equal, what is the probability of getting 3 males?
ans: using binomial probability distribution formula:

10. 5.3 Binomial Distributions
calculate the expected value for trying a test 4 times if you have a 60% chance of passing each time
ans: E(x) = np = 4(0.60) = 2.4
so you are expected to pass 2.4 tests

11. 5.4 Normal Approximation of Binomial Distribution
calculate σ and the mean, given the number of trials and the probability
determine whether a binomial random variable can be approximated by a normal distribution (p308)
calculate probabilities of data points or ranges of data, given the number of trials and the probability using z-scores

12. 5.4 Normal Approximation of Binomial Distribution
ex: Mr. Greer tosses a die 100 times. What is the probability of less than 15 sixes?
ans:

13. 5.4 Normal Approximation of Binomial Distribution
ex: what is the probability of Mr. Greer getting between 15 and 20 sixes?
ans:

14. 5.5 Simulations
will not be covered in examination