Starter A mother has to pack 3 school lunches into 3 different school bags. She never remembers which lunch box belongs to which school bag. If X is the number of lunch boxes that go into the correct school bag, complete a probability distribution for X. x 1 2 3 P(X=x) 2/6 3/6 1/6

John Venn 1834-1923 Venn’s most important work was in logic and probability. He introduced his now famous Venn Diagram. This showed how a number of closed curves (circles) could be used to represent sets with something in common. Venn had other skills and interests too, including a rare skill in building machines. He used his skill to build a machine for bowling cricket balls which was so good that when the Australian Cricket team visited Cambridge in 1909, Venn's machine clean bowled one of its top stars four times.

Note 3 : Venn Diagrams Venn diagrams show relationships between two or more events. The rectangle represents the sample space and the circles represent events.

The intersection A ∩ B represents both occurring. A and B.

Example: The probability that a student in the stats class plays cricket is 0.8. The probability a student plays rugby is 0.35. The probability that the student plays both sports is 0.24. Calculate the probability that a student plays only one sport. P(C) = 0.8 P(R) = 0.35 P(C ∩ R) = 0.24

P(C) = 0.8 P(R) = 0.35 P(C ∩ R) = 0.24 C R 0.56 0.24 0.11 0.09 P(one sport) = P(Cricket) + P(Rugby) = 0.56 + 0.11 = 0.67

Workbook Page 156 Exercise B, Q1-6