1 Press Ctrl-A ©G Dear2009 – Not to be sold/Free to use Tree Diagrams Stage 6 - Year 12 General Mathematic (HSC)

2 should They should be used when multi-stage events occur. sample space They can be used to list the sample space. Find the Sample Space for tossing three coins H T H T H T H T H T H T H T Event 1 Event 2 Event 3 S= { HHH,HHT,HTH,HTT, THH,THT,TTH, TTT TTT } n(S) = Number of elements in the sample space Probability of only two tails P(Only Two Tails) = 3 8 Probability of three heads P(HHH) = 1 8 Coin Toss Button

3 firsteffectevent The first event may effect the second event. Four 14 Four cards have the numbers 1 to 4 on them. tree diagram2 digit Draw a tree diagram to list all 2 digit numbers that can be formed. Event 1 Event S= { 12,12,12,12, 13,13,13,13, 14,14,14,14, 21,21,21,21, 23,23,23,23, 24,24,24,24, 31,31,31,31, 32,32,32,32, 34,34,34,34, 41,41,41,41, 42,42,42,42, 4343}4343} ) = 12 n(S) = 12 ) = P(Even) = 6 12 = 1212

4 firstsecond event different The first and second event may be different. We can toss a coin and roll a dice We can toss a coin and roll a dice. Event 1 Event H T S= { H1,H1,H1,H1, H2,H2,H2,H2, H3,H3,H3,H3, H4,H4,H4,H4, H5,H5,H5,H5, H6,H6,H6,H6, T1,T1,T1,T1, T2,T2,T2,T2, T3,T3,T3,T3, T4,T4,T4,T4, T5,T5,T5,T5, T6T6}T6T6} ) = 12 n(S) = 12 ) = P(H,<4) = 3 12 = 1414