The Mods and Rockers Guide to Conditional Tree Diagrams

1
The Mods and Rockers Guide to Conditional Tree
Diagrams Multiplication Rule In the
1960s,young people were divided into mods or
rockers. Mods rode motor scooters and rockers
rode motorbikes. If Derby mods wanted to go to
the Twisted Wheel through Matlock or club in
Manchester, they would have to pass through
Matlock or Ashbourne. Matlock was rocker
territory so beware! Probability of Matlock P(M)
0.2 Probability of Ashbourne P(M) 0.8
Probability of Rockers at Matlock P(R)
0.8 Probability of Rockers at Ashbourne P(R) 0.4
2
Draw a tree diagram and calculate P(MR)
Probability of Matlock P(M) 0.2 Probability of
Ashbourne P(M) 0.8 Probability of Rockers at
Matlock P(R) 0.8 Probability of Rockers at
Ashbourne P(R) 0.4
Did you see any rockers?
Yes!
The probability that you passed through Matlock
is..
3
0.2 x 0.8 0.16
R
0.8
M
0.2 x 0.1 0.02
R
0.2
0.1
0.4
0.8 x 0.4 0.32
R
M
0.8
R
0.6
0.8 x 0.6 0.48
P(M n R) P(MR) x P(R) 0.16 P(MR) x
0.48 P(MR) 0.16 0.48 ? P(MR) 0.333
4

• A keep fit enthusiast swims, runs or cycles each
  day with a probabilities 0.2, 0.3 and 0.5
  respectively. If he swims then he spends time in
  the sauna with a probability of 0.35. The
  probability that he spend time in the sauna after
  running or cycling is 0.2 and 0.45 respectively.
• Represent this on a tree diagram
• Find the probability that on any particular day
  he uses the sauna
• Given that he uses the sauna, find the
  probability that he has been swimming on that day
• Given that he did not use the sauna one day, find
  the probability that he has been swimming

5
b) Find the probability that on any particular
day he uses the sauna
P(sauna) 0.07 0.06 0.225 ? P(sauna)
0.355
0.07
0.35
S
W
0.65
0.13
0.2
NS
0.2
S
0.06
0.3
R
0.8
0.24
NS
0.5
0.45
S
0.225
C
0.55
0.275
NS
6
c) Given that he uses the sauna, find the
probability that he has been swimming on that day
P(W ? S) P(WS) x P(S) 0.07 P(WS) x
0.355 P(WS) 0.197 ? 0.20
P(S) 0.355
0.07
0.35
S
W
0.65
0.13
0.2
NS
0.2
S
0.06
0.3
R
0.8
0.24
NS
0.5
0.45
S
0.225
C
0.55
0.275
NS
7
d) Given that he did not use the sauna one day,
find the probability that he has been swimming
P(W ? NS) P(WS) x P(NS) 0.13 P(WNS) x
0.645 P(WNS) 0.202
P(NS) 0.645
0.07
0.35
S
W
0.65
0.13
0.2
NS
0.2
S
0.06
0.3
R
0.8
0.24
NS
0.5
0.45
S
0.225
C
0.55
NS
0.275