Introduction to Probability Pearson: Chapter 10 p336 - 350 Homework: Exercise 10.3 Q1, 2, 4, 5, 6 Haese & Harris: Chapter 19 Homework: Exercise 19 C Q 1-7, 10 p477, 478

Key Definitions Outcomes = The possible events, what we observe Sample space, U = all the possible outcomes Eg Sample space for rolling a dice: _________________________________ Theoretical Probability of an event A occurring, P(A): 0 ≤ P ≤ 1 where P = 0 is an impossible event & P = 1 is a certain event Expected Outcome: Eg. a)What is the probability of throwing a prime number on a 6-sided dice? b) If the dice is rolled 10 times, how many prime numbers would you expect?

Definitions Experimental Probability = for events where the probability can’t be predicted, and instead is calculated from collected data. The probability of an event can only be determined by a large number of trials. Relative Probability = probability obtained by experiment or from data. This is an estimate, the larger the number of trials, the more accurate it will be.

Venn Diagrams Sample Space = Universal Set, U = rectangle around the diagram Set A = Event A = usually represented as a labeled circle Complement of A = A’ = Complementary Event A = “not A” – the area outside of the set A. Intersection of Set A and B = A ∩ B = in A and B Union of Set A and B = A ∪ B = in A or B (or in both)

Venn Diagram Questions 1. This diagram shows the numbers of students taking the IB diploma in a school and also the numbers attending lessons in certain subjects. The classes are represented by sets S: {Math}, G: {German} and M: {Music} S G M 22 8 x 9 6 3 13 73 U Find the number of IB students studying: None of the 3 subjects Music and German but not math studies Music or German, but not both Math studies or music but not German All three subjects, if there are 136 students in this sample.

Venn Diagram Questions In a class of 30 students, 15 own a bicycle, 10 own a car and 2 own both. Draw a Venn diagram to represent this information. Find the probability that a randomly chosen student owns either a bicycle or a car. Find the probability that a a randomly chosen student owns neither a bicycle or a car?

Combined Events 1. If P(A) = 0.6, P(A∪B) = 0.7 and P(A ∩ B) = 0.3, find P(B) A B If P(A) = 0.6, P(A∪B) = 0.3 and P(A ∩ B) = 0.2, find a) P(A∪B) b) P(B’) c) P(A∩B’ A B

Combined Events In a group of 18 students, 11 have an Instagram account, 8 have a twitter account and 2 have neither. The following Venn diagram shows the events “uses Instagram” and “uses twitter”. The values p, q, r, and s represent numbers of students. Instagram twitter a) (i) Write down the value of p. (ii) Find the value of q. (iii) Write down the value of r and s. b) A student is selected at random from the class. (i) Write down the probability that the student has an Instagram account. (ii) Find the probability that this student uses Instagram or twitter but not both.