Win – W Loss – L 7W7W 11 W 2L2L 3L3L 12 L 7 not on 1 st roll - L 1 st sum Repea ted W Total Wins:

Simulation Use simulation techniques to represent 25 games of “crops” What is the relative frequency of wins? randInt(2,12,25) sto L1 Count wins, record Count losses, record Delete both from L1 randInt (2, 12, ??? number left over after wins and losses are removed from list) sto in L2 Count as wins the ones where the same sum is repeated. Count as losses the ones where the sum is 7. Repeat until all are wins or losses.

7 or 11 Based on your data – what is the relative frequency of rolling a sum of 7? What is the relative frequency of rolling a sum of 11? Which of these sums appears more likely to occur?

2,3, or 12 What is the relative frequency of rolling a 2? What is the relative frequency of rolling a 3? What is the relative frequency of rolling a 12? Based on your results which of these seems more likely to occur?

What is the actual probability of rolling a sum of 7? A sum of 11? A sum of 2? A sum of 3? A sum of 12?

AP Statistics Chapter 7 Section 1

Vocab Random variable Discrete random variable – probability distribution lists the values and their probabilities Probability distribution – looks different for discrete and continuous variables Probability histogram – can only be used with discrete variables Continuous random variable – probability distribution is described by a density curve. The probability of any event is the area under the density curve and above the values of X that make up the event.

Probability Distribution 1.List Sample Space 2.Assign probabilities to events in the sample space Review: 0<P(X)<1 P(S) = 1

GradesABCDF Probability Discrete or continuous? What is the probability that a student gets a B or better in this class? 40% 30% 20% 10% A B C D F

Create the probability distribution of the discrete random variable X that counts the number of heads in four tosses of a coin. HTHT THTH HTTT THHTHHTH THTTHTTHHTHH TTHTHHTTHHHT TTTTTTTHTTHHTHHHHHHH # of heads01234 Probability

P(0.4<X<0.6) = 0.2

Normal distributions are probability distributions. An opinion poll asks an SRS of 1500 American adults what they consider to be the most serious problem facing our schools. 30% say “drugs”. What is the probability that the poll result differs from the truth about the population by more than 2 % points?

The probability that the poll result differs from the truth by more than 2% points is approx. 9%.