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.