Originally Posted by

**Chez_**

Hi, can someone help me draw the right venn or tree diagram for these questions please. Iv drawn a few diagrams and woorked things out and got the answer but then realised id written the wrong numbers out first.

100 cars are entered for a road-worthiness test which is in 2 parts mechanical and electrical. A car can only pass if it passes both parts.

Half the cars fail the electrical test and 62 pass the mechanical. 15 pass the elctrical but fail the mechanical test.

Find the probability that a car chosen at random

i) pass overall

ii)fails one test only

iii)given that it has failed , failed the mechanical test only.

Thank you

E = Electrical Test

M = Mechanical Test

P(E' n M) = $\displaystyle \frac{27}{100}$

P(E n M') = $\displaystyle \frac{15}{100}$

P(E' n M') = $\displaystyle \frac{23}{100}$

i) P (E n M) = $\displaystyle \frac{100 - (27 + 15 + 23)}{100} = \frac{35}{100}$

ii) P (Passes One Test) = $\displaystyle \frac{15+27}{100} = \frac{42}{100}$

iii) P (E n M' / Failed One Test) = $\displaystyle \frac{15}{100} \div \frac{65}{100} = \frac{15}{65}$

In the venn diagram below, E = 15, M = 27 and the number outside the venn diagram is P(E' n M').

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$\displaystyle

\begin{picture}(50,50)

\put(80,80){\circle{40}}

\put(100,80){\circle{40}}

\put(85,75){35}

\put(65,70){E}

\put(105,70){M}

\end{picture}

23

$

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