The probabilities that drivers A, B and C will drive home safely after consuming liquor are 2 / 5, 3 / 7 and 3 / 4, respectively. What is the probability that they will drive home safely after consuming liquor ?

Let A be the event of driver A drive safely after consuming liquor. 

Let B be the event of driver B drive safely after consuming liquor. 

Let C be the event of driver C drive safely after consuming liquor. 

P(A)=2/5,P(B)=3/7,P(C)=3/4

The events A, B and C are independent . Therefore,

$PA\cap B\cap C=P\left(A\right)P\left(B\right)P\left(C\right)=\frac{2}{5}*\frac{3}{7}*\frac{3}{4}=\frac{9}{70}$

Therefore, The probability that all the drivers will drive home safely after consuming liquor is 9/70