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Conditional Probability
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Can you improve your chances of passing your theory test by using an app?
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A company has produced an app which it thinks will help people pass their driving theory test.
Results show that the number of people passing the theory test is higher if they have used the app before sitting the test and that the number of people using the app is roughly equal to those who don’t use it.
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Will you do some extra work to pass?
Toss a coin.
If you get a head you will use the app to help.
If you get a tail you won’t use the app.
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Will you pass the theory test first time?
This example is different to the last one as this time the second event is dependent on the first one.
The probability of passing changes if you use the simulator.
This is called conditional probability.
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If you used the app
Throw a dice.
If you get 1, 2, 3, 4 or 5 then you pass the test.
If you get a 6 then you don’t.
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If you didn’t use the app
Throw 2 dice and add the scores.
If you get a total of 2, 3, 4, 5, or 6 then you pass the test.
If you get a score of 7, 8, 9, 10, 11 or 12 then you don’t.
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Probability
There are 2 outcomes when toss a coin
The probability of using the app =
If you had 72 people how many would you expect to use the app?
Answer 36 to use it and 36 to not use it.
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Tree diagram
Pass
Yes
Not pass
72 people
Pass
No
Not pass
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Number using the app
Theory test results
36
36
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ProbabilityWhat is the probability of passing the theory if the app was used?
5 choices out of 6 so
Out of the 36 people how many would you expect to pass?
Answer: 30 to pass and 6 not to pass.
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Tree diagram
Pass
Pass
Not pass
72 people
Pass
Not pass
Not pass
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Number passing theory first time
Number passing practical first time
36
36
30
6
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How many of the 36 people who didn’t use the app would you expect to pass the practical first time?
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Probability
There are 36 outcomes when you roll 2 dice and add the scores.
15 of these totals are 2, 3, 4, 5, 6
The probability of passing = =
Out of the 36 people how many would you expect to pass?
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Answer
Answer: 15 to pass and 21 not to pass.
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Tree diagram
Pass
Yes
Not pass
72 people
Pass
No
Not pass
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Number using the simulator
Number passing practical first time
36
36
30
6
15
21
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Answering questionsYou can now use the tree diagram to answer questions on probability.
You have all the information you need on it.
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Why was 72 a good number to start with?
When you draw tree diagrams you may have to decide a number of people to start with.• The first probability was out of 2 (halves) and 72
divides by 2 to give 36.• The second probabilities were out of 36 and 6
and 36 divides by 36 and 6.• 72 was a good number of students to choose as
it divides by 2 and the result divides by 6 and 36
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