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Tree Diagrams and Independent events

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by

Mr Mattock

on 5 November 2016

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Transcript of Tree Diagrams and Independent events

The sample space below shows the result of flipping two coins.





Write down the probability of getting the same on both coins.
1/2
What happens if one or both of the coins is biased?
You
need to add a lot more rows/columns.
The sample space below shows the result of flipping two coins.





Write down the probability of getting the same on both coins.
What happens if one or both of the coins is biased?
Tree Diagrams and Independent events
Starter
Using tree diagrams
Tree diagrams
Two biased coins are flipped. The probability of heads on the first coin is 0.6. The probability of heads on the second coin is 0.75. Show the probabilities of the four possible outcomes.






Work out the probability of getting two coins the same.
L.O. - Use tree diagrams to find the probability of combined events.
Starter
H
T
H
H
T
T
P(H, H)
P(H, T)
P(T, H)
P(T, T)
0.6
0.75
0.75
Tree diagrams
Two biased coins are flipped. The probability of heads on the first coin is 0.6. The probability of heads on the second coin is 0.75. Show the probabilities of the four possible outcomes.






Work out the probability of getting two coins the same.

0.15 + 0.3 = 0.45
H
T
H
H
T
T
P(H, H) = 0.45
P(H, T) = 0.15
P(T, H) = 0.3
P(T, T) = 0.1
0.6
0.75
0.75
0.4
0.25
0.25
Team A and B play each other in the league home and away. Each game can be win, lose or draw. Draw a tree diagram to show the possible outcomes for Team A.






The probability that team A win their home game is 0.7. The probability of a draw is 0.12. The probability that team A win their away game is 0.4. The probability of a draw is 0.38. Work out the probability that Team A get the same result from both games.
Using tree diagrams
Team A and B play each other in the league home and away. Each game can be win, lose or draw. Draw a tree diagram to show the possible outcomes for Team A.






The probability that team A win their home game is 0.7. The probability of a draw is 0.12. The probability that team A win their away game is 0.4. The probability of a draw is 0.38. Work out the probability that Team A get the same result from both games.
W
W
W
W
D
D
D
D
L
L
L
L
0.7
0.12
0.18
0.4
0.4
0.4
0.38
0.38
0.38
0.22
0.22
0.22
P(W,W) = 0.28
P(D,W) = 0.048
P(L,W) = 0.072
P(W,D) = 0.266
P(D,D) = 0.0456
P(D,D) = 0.0684
P(W,L) = 0.154
P(D,L) = 0.0264
P(L,L) = 0.0396
0.28 + 0.048 + 0.072 = 0.4
Activity
Complete the tree diagram worksheet
Plenary
Complete the exam question.
Plenary
Activities
Activity
Answers

Key
Examples

Worked
Example

Worked
Example
Full transcript