Statistics- S1 Probability

I was wondering if anybody could help me with this question. i am taking OCR MEI S1 and i'm sure the question is really easy but i don't know how to tackle this question:

100 cars are are entered for a road-worthiness test which is in 2 parts, mechanical and electrical. A car passes only if it passes both parts. Half the cars fail the electrical test and 62 pass the mechanical. 15 pass the electrical test but fail the mechanical test.

Find the probability that a car chosen at random
i) passes overall
ii)fails on one test only
iii)given that it has failed, failed the mechanical test only.

The answers are as follows:
i)35/100
ii)42/100
iii)15/65

if anyone could explain this to me i'd be really grateful!
Thanks xXx

Reply 1

Libertine

KymmyC

100 cars are are entered for a road-worthiness test which is in 2 parts, mechanical and electrical. A car passes only if it passes both parts. Half the cars fail the electrical test and 62 pass the mechanical. 15 pass the electrical test but fail the mechanical test.

Find the probability that a car chosen at random
i) passes overall
ii)fails on one test only
iii)given that it has failed, failed the mechanical test only.
The answers are as follows:
i)35/100
ii)42/100
iii)15/65

23 fail both
35 pass both
15 pass electric, fail mechanical
27 pass mechanical, fail electric
i) 35/100 (obviously)
ii) (15+27)/100 = 42/100
iii) Prob(failed mech, passed electric)/Prob(it failed at least one)
= 15/100/65/100
= 15/65

Reply 2

KymmyC