Question

The ratio of the number of trucks along a highway, on which a petrol pump is located, to the number of cars running along the same highway is 3 : 2. It is known that an average of one truck in thirty trucks and two cars in fifty cars stop at the petrol pump to be filled up with the fuel. If a vehicle stops at the petrol pump to be filled up with the fuel, find the probability that it is a car

• A. $\frac{4}{9}$
• B. $\frac{9}{250}$
• C. $\frac{3}{5}$
• D. $\frac{1}{30}$

Answer 1

Answer: (A)

$\frac{4}{9}$

C : Vehicle is Car $P\left(\overline{C}\right)=2/5$
$\overline{C}$ : Vehicle is Truck $P\left(C\right)=3/5$
E : Vehicle stops for fuel $P\left(E/C\right)=2/50$
$P\left(\overline{E}/\overline{C}\right)=1/30$
$P\left(E\right)=P(CE\cup C\overline{E})$
$=P\left(CE\right)+P\left(\overline{C}E\right)$
$=\frac{2}{5}\left(\frac{2}{50}\right)+\frac{3}{5}.\frac{1}{30}=\frac{1}{10}[\frac{4}{25}+\frac{1}{5}]=\frac{9}{250}$
$P\left(C/E\right)=\frac{P\left(CE\right)}{P\left(E\right)}=\frac{4/250}{9/250}=\frac{4}{9}$