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 ?
Solution
Correct Answer: Option C
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,
\(P\left(A\cap B\cap C\right)=P(A)P(B)P(C)=\frac25\times\frac37\times\frac34=\frac9{70}\)
Therefore, The probability that all the drivers will drive home safely after consuming liquor is 9/70
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