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General Mathematic (HSC) Tree Diagrams Stage 6 - Year 12 Press Ctrl-A ©G Dear2009 – Not to be sold/Free to use 1 They should be used when multi-stage events occur. They can be used to list the sample space. Find the Sample Space for tossing three coins Event 1 Event 2 Event 3 S={ HHH, HHT, HTH, HTT, H 1 THH,THT,TTH, TTT } H T 2 H H 3 Probability of only two tails T T 4 P(Only Two Tails) = 3 H 5 8 Number of H T 6 T elements in the heads Probability of three 7 H T sample space.1 T 8 P(HHH) = 8 n(S) = 8 Coin Toss Button 2 The first event may effect the second event. Four cards have the numbers 1 to 4 on them. Draw a tree diagram to list all 2 digit numbers that can be formed. Event 1 Event 2 2 1 3 4 1 2 3 4 1 3 2 4 1 4 2 3 S={ 12,13,14,21,23,24, 31,32,34,41,42,43} 1 2 3 4 n(S) = 12 P(Even) = 6 12 =1 2 3 The first and second event may be different. We can toss a coin and roll a dice. Event 1 Event 2 1 2 3 H 4 5 6 1 2 3 T 4 5 6 S={ H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6} n(S) = 12 P(H,<4) = 3 12 =1 4 4