Statistics 1 Revision Notes - Mr Barton Maths
Statistics 1 Revision Notes - Mr Barton Maths
Statistics 1 Revision Notes - Mr Barton Maths
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Tree diagrams<br />
The rules for tree diagrams are<br />
Select which branches you need<br />
Multiply along each branch<br />
Add the results of each branch needed.<br />
Make sure that you include enough working to show which branches you are using (method).<br />
Be careful to allow for selection with and without replacement.<br />
Example: In the launch of a rocket, the probability of an electrical fault is 0⋅2. If there is an<br />
electrical fault the probability that the rocket crashes is 0⋅4, and if there is no electrical<br />
fault the probability that the rocket crashes is 0⋅3.<br />
Draw a tree diagram. The rocket takes off, and is seen to crash. What is the<br />
probability that there was an electrical fault?<br />
Solution:<br />
We want to find P(E⏐C).<br />
P(E⏐C) = <br />
<br />
P(E∩C) = 0⋅2 × 0⋅4 = 0⋅08<br />
and P(C) = 0⋅2 × 0⋅4 + 0⋅8 × 0⋅3 = 0⋅32<br />
0⋅2<br />
E<br />
0⋅4<br />
0⋅6<br />
C<br />
C′<br />
⇒<br />
P(E⏐C) = <br />
= 0⋅25 C′<br />
0⋅8<br />
0⋅3<br />
C<br />
E′<br />
0⋅7<br />
14/04/2013 <strong>Statistics</strong> 1 SDB 25
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