Tree Diagrams – Mixed – Demonstration

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Presentation transcript:

Tree Diagrams – Mixed – Demonstration This resource provides animated demonstrations of the mathematical method. Check animations and delete slides not needed for your class.

25 41 16 100 20 59 39 P (Only Art) = 20 100 art geography not art art Frequency Trees ① 100 Year 11 students were surveyed about whether they studied geography or art. 41 students studied geography. 25 students studied geography and art. 39 students didn’t study geography or art. If you pick a student at random, what is the probability they only study art? P (Only Art) = 20 100 art 25 41 geography 16 not art 100 art 20 59 not geography 39 not art

Unconditional Probability Trees ② Box & Marbles There are black and white marbles in the box. One is picked – and replaced – then another is picked. What is the probability of picking two black marbles? P (BB) = 9 100 1st Pick 2nd Pick Result 3 10 3 10 × 3 10 = 9 100 Black BB 3 10 Black 3 10 × 7 10 = 21 100 7 10 White BW 3 10 7 10 × 3 10 = 21 100 Black WB 7 10 White 7 10 × 7 10 = 49 100 7 10 White WW

Conditional Probability Trees ③ Box & Marbles There are black and white marbles in the box. One is picked – and not replaced – then another is picked. What is the probability of picking two black marbles? P (BB) = 6 90 1st Pick 2nd Pick Result 2 9 3 10 × 2 9 = 6 90 Black BB 3 10 Black 3 10 × 7 9 = 21 90 7 9 White BW 3 9 7 10 × 3 9 = 21 90 Black WB 7 10 White 7 10 × 6 9 = 42 90 6 9 White WW

Conditional Probability Trees ④ The probability Jack passes his 1st Geography test is 0.7 If he passes the 1st test, the probability he passes the 2nd test is 0.8 If he fails the 1st test, the probability he passes the 2nd test is 0.6 What is the probability he passes only one of the tests? P(Pass one, Fail one) = 0.14+0.18 = 0.32 1st Test 2nd Test Result 0.8 PP 0.7 ×0.8=0.56 Pass Pass 0.7 0.2 Fail PF 0.7 ×0.2=0.14 0.6 Pass FP 0.3 ×0.6=0.18 0.3 Fail Fail FF 0.3 ×0.4=0.12 0.4

tom@goteachmaths.co.uk Questions? Comments? Suggestions? …or have you found a mistake!? Any feedback would be appreciated . Please feel free to email: tom@goteachmaths.co.uk