1. Chapter 5 Review MDM 4U
Mr. Lieff

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) 35

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

7. 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) = 343/4096 = 0.084

8. 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:

9. 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

10. 5.4 Normal Approximation of Binomial Distribution
determine whether a binomial random variable can be approximated by a normal distribution (p. 308)
calculate and σ, given the number of trials and the probability
calculate probabilities of data points or ranges of data, given the number of trials and the probability using z-scores

11. 5.4 Normal Approximation of Binomial Distribution
ex: Mr. Lieff tosses a die 100 times. What is the probability of less than 15 sixes?
ans:
From the z-score table, the probability is 28.1%

12. 5.4 Normal Approximation of Binomial Distribution
ex: what is the probability of Mr. Lieff getting between 15 and 20 sixes?
ans: