Edexcel gcse maths higher probability tree question - driving test

The question was as follows:
Someone takes a driving test in two parts, a theory and a practical
the probability of passing the theory test is 0.75
the probability of passing only one of the test is 0.36
the two events are independent.
find the probability of passing the practical test
What I did was draw a tree and label the unknowns x and y. the I set up two equations: 2x+2y=1 and 0.75x+0.25y=0.36.
then I did simultaneous equations to get an answer of 0.03
I don't know if this is right or wrong so can someone please let me know if its right or wrong and what i may have done wrong.

Reply 1

gcsesaremeh

3

(Original post by hamzafarrukh0)The question was as follows:
Someone takes a driving test in two parts, a theory and a practical
the probability of passing the theory test is 0.75
the probability of passing only one of the test is 0.36
the two events are independent.
find the probability of passing the practical test
What I did was draw a tree and label the unknowns x and y. the I set up two equations: 2x+2y=1 and 0.75x+0.25y=0.36.
then I did simultaneous equations to get an answer of 0.03
I don't know if this is right or wrong so can someone please let me know if its right or wrong and what i may have done wrong.

idk but i got the final answer of passing it as 0.52
what i did was i did 0.36/0.75 to get 0.48. i then took 0.48 from 1.00 to get 0.52. i dunno if this is right but my mate got the same answer as me.

Reply 2

Muttley79

20

What are x and y? You haven't defined them at all

Original post by hamzafarrukh0

The question was as follows:
Someone takes a driving test in two parts, a theory and a practical
the probability of passing the theory test is 0.75
the probability of passing only one of the test is 0.36
the two events are independent.
find the probability of passing the practical test
What I did was draw a tree and label the unknowns x and y. the I set up two equations: 2x+2y=1 and 0.75x+0.25y=0.36.
then I did simultaneous equations to get an answer of 0.03
I don't know if this is right or wrong so can someone please let me know if its right or wrong and what i may have done wrong.

Reply 3

JacobPC

3

I got 0.52 too!!!! But everyone’s saying it’s 0.72…..

Reply 4

Jacob V

7

I saw the answer to be 0.78 but idk how they got it. I check used the answer to check backwards and everything checks out.
0.25 (1/4) X 0.78 = 0.195
1-0.78 = 0.22
0.75 (3|4) X 0.22 = 0.165
0.165 + 0.195 = 0.36
0.36==0.36
Therfore the passing probability for passing is 0.78 or 78%

Reply 5

gdunne42

21

Original post by hamzafarrukh0

The question was as follows:
Someone takes a driving test in two parts, a theory and a practical
the probability of passing the theory test is 0.75
the probability of passing only one of the test is 0.36
the two events are independent.
find the probability of passing the practical test
What I did was draw a tree and label the unknowns x and y. the I set up two equations: 2x+2y=1 and 0.75x+0.25y=0.36.
then I did simultaneous equations to get an answer of 0.03
I don't know if this is right or wrong so can someone please let me know if its right or wrong and what i may have done wrong.

If the probability of passing is x, the probability of failing is (1 - x) seems to be the way most people have successfully attacked the question
Using your interesting method x + y = 1

(edited 1 year ago)

Reply 6

haza1232

3

Original post by Jacob V

I saw the answer to be 0.78 but idk how they got it. I check used the answer to check backwards and everything checks out.
0.25 (1/4) X 0.78 = 0.195
1-0.78 = 0.22
0.75 (3|4) X 0.22 = 0.165
0.165 + 0.195 = 0.36
0.36==0.36
Therfore the passing probability for passing is 0.78 or 78%

I got that too :smile:

Reply 7

Αbsolute

2

Alright, I think there is a large misconception in this thread so let me clear up the question for any onlookers:

A driving test has two parts, a theory and a practical test.
The probability of passing the theory test is 0.75
The probability of passing only one of the two parts is 0.47

The two events are independent.

Work out the probability of passing the practical test

1.

Firstly, we will define the probability of passing the theory test as P₁ (P₁= 0.75)

2.

We will also define the probability of failing the theory test as P₂ (P₂ = 0.25)

3.

Along with the two unknowns: x = Failing the practical test y = Passing the practical test

4.

We can now create the formula: P₁ × x + P₂× y = 0.47

5.

As y = 1 - x we swap y for this: P₁ × x + P₂× (1 - x) = 0.47

6.

And swap in the values for P₁ & P₂ : 0.75 × x + 0.25(1 - x) = 0.47

7.

Now simplify: 0.75x + 0.25 - 0.25x = 0.47

8.

Simplify for x (minus 0.47 by 0.25): 0.5x = 0.22

9.

Therefore: x = 0.44

10.

We can now find y: 1 - 0.44 = 0.56

This means the answer to the question is 56%

Note: This question can be tackled to where you can define x as passing and swap the values like so

0.25x + 0.75(1 - x) = 0.47
-0.5x = -0.28
x = 0.56

However, I believe this method may cause mistakes but it is equally as valid.

Edexcel gcse maths higher probability tree question - driving test

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