Question

On friday night $20\%$ of all the techies in India are under the influence of alcohol.The probability that the person will have an accident under the influence of alcohol is 0.001.The probability that a sober person will meet an accident is 0.0001.If the car on friday night smashed into the tree,the probability that the driver was under the influence of alcohol is?

• A. 4/7
• B. 2/7
• C. 5/7
• D. 10/21

Answer 1

The correct option is C

5/7

P(X)= Techie met an accident

$Y_1=Hewasalcoholic:\frac{1}{5}$

$Y_2=Hewassober=\frac{4}{5}$

$P\left(\frac{X}{Y_1}\right)=0.001$

$P\left(\frac{X}{Y_2}\right)=0.0001$

$P\left(\frac{Y_1}{X}\right)=\frac{\left(0.2\right)\times \left(0.001\right)}{\left[\right(0.2\times 0.001)+(0.8\times 0.0001\left)\right]}$= $P\left(\frac{Y_1}{X}\right)=\frac{5}{7}$