Chapter 5 Review MDM 4U Mr. Lieff

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

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

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

5.2 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

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

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

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:

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

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

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%

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