Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I am working on a maths exercise and came across this question:

Given: A motorist which causes an accident, must submit to a blood test. Research shows that 1% of the drivers which cause crashes, driving under influence (alcohol, drugs). There is a chance of 75% that someone under influence is tested positive. However, there is a chance of 5% that someone who is sober is tested positive.

Wanted: (a) What is the probability that someone is under influence if the test was positive? (b) What is the probability that someone is sober, while the test was negative?

So i tried calculating these questions. a: ((0.75*0.01) /( 0.75 * 0.01 + 0.25 * 0.99)) = 0.029 or ((0.75*0.99) /( 0.75 * 0.99 + 0.25 * 0.01)) = 0.996

For b: ((0.05*0.01) /( 0.05 * 0.01 + 0.95 * 0.99))

Are these answers correct? My maths skills are terrible any help is appreciated,



Ps. My first language isn't english.

share|cite|improve this question
up vote 1 down vote accepted

For a:

(is under infulence & test was positive) / ((is under influence & test was positive) + (is sober & test was positive).

It gives us: $( 0.01 \cdot 0.75) /(0.01 \cdot 0.75 + 0.99 \cdot 0.05)$. (0.99 is 100% minus 1% of influenced ones).

For b:

(is sober & test was negative) / ((is sober & test was negative) + (is under influence & test was negative))

So it is: $(0.99 \cdot 0.95) /( 0.99 \cdot 0.95 + 0.01 \cdot 0.25)$. (0.25 is 100%-75% because people under influence are tested positive with probability 75% so tested negative with probability of 100%-75%=25%).

In general: in numerator you put the probability of your specific event (like "is sober and was testes negative") and in the the denominator you put the probability of a more general event which is known/assumed as true (like "was tested positive" - you know the result of the test) - probability of this general event is a sum of probabilities of some smaller events including your specific event.

share|cite|improve this answer
Thanks for your help and explanation! Appreciated very much!! – Jef Dec 22 '11 at 22:47

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.