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

2. 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) =
art 25 41
geography 16
not art
100
art 20 59
not geography 39
not art

3. Unconditional Probability Trees②
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) =
1st Pick
2nd Pick
Result
3 10
3 10 × = 9 100
Black BB
3 10
Black
3 10 × =
7 10
White BW
3 10
7 10 × =
Black WB
7 10
White
7 10 × =
7 10
White WW

4. Conditional Probability Trees③
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) =
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

5. Conditional Probability Trees④
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) = = 0.32
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

8. tom@goteachmaths.co.uk Questions? Comments? Suggestions?
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