Venn Diagram Question

[S_100]

'100 cars are entered for a roadworthieness test which is in two parts, mechanical and electrical. A car passes only if it passes both parts. Half the cars fail the electrical test and 62 pass the mechnical test. 15 pass the electrical but fail the mechanical test.'

What is the probabliity a car chosen at random passes overall?

I drawed a Venn Diagram attached. What I don't understand is why the intersect is calculated by 50 - 15 = 35, and why 62 is the M and E Complement region.

My intial method was to start with backwards , starting with the statement,
'15 pass the electrical but fail the mechanical test.' ---> n (E AND M') = 15

but with the statement, 62 passed mechanical and half cars fail electrical I was unsure.

I am also stuck on how it can be decuded from the quoted statement, that n ( (E AND M) = 50-15

 

[pka]

'100 cars are entered for a roadworthieness test which is in two parts, mechanical and electrical. A car passes only if it passes both parts. Half the cars fail the electrical test and 62 pass the mechnical test. 15 pass the electrical but fail the mechanical test.'
What is the probabliity a car chosen at random passes overall?

Lets setup some notation. There are four sets to consider. Suppose \(E\) is that pass electrical, \(M\) the set passing mechnical, \(E\cap M\) both,
\(E\setminus M\), electrical but not mechanical, \( M\setminus E\), mechanical but not electrical and finally \(N\) is set of cars not passing either.
Now for numbers
\(\|E\setminus M\|+\|E\cap M\|+\|M\setminus E\|+\|N\|=100\)
\(\|E\setminus M\|=15\)
\(\|M\setminus E\|+\|N\|=50\) Half do not pass the electrical.
Can you finish?

 

[HallsofIvy]

100 cars are entered for a roadworthieness test which is in two parts, mechanical and electrical. A car passes only if it passes both parts. Half the cars fail the electrical test and 62 pass the mechnical test. 15 pass the electrical but fail the mechanical test.

Of 50 cars that passed the electrical test, 15 did not pass the electrical test so 50- 15= 35 cars also passed both the electrical and mechanical tests.

 

[Steven G]

Of 50 cars that passed the electrical test, 15 did not pass the electrical test

I had to read that three times. Each time I got a bit more dizzy.

 

[HallsofIvy]

Probably because of all the electricity in the air!

 

[mcstatz5829]

	Pass Electrical	Fail Electrical	row sum
Pass Mechanical			62
Fail Mechanical	15
column sum	50	50

Venn diagram is the wrong setup. You need a 4x4 grid and to fill in the blanks. I added an extra column to sum the rows, and an extra row to sum the columns.

I put in the information contained in the question.

Theoretically you should be able to fill in the blanks and come up with the answer.

 

[frjones]

	Pass Electrical	Fail Electrical	row sum
Pass Mechanical			62
Fail Mechanical	15
column sum	50	50

Venn diagram is the wrong setup. You need a 4x4 grid and to fill in the blanks. I added an extra column to sum the rows, and an extra row to sum the columns.

I put in the information contained in the question.

Theoretically you should be able to fill in the blanks and come up with the answer.

Exactly, you're right. Will need a 4x4 grid and venn diagram won't make it. Thanks.