Question

In a given day in the rainy season, it may rain 70% of the time. If the rains, chance that a village fair make a loss on that day is 80%. However, if it does not rain, chance that the fair will make a loss on that day is only 10%. If the fair has not made a loss on a given day in the rainy season, what is the probability that it has not rained on that day?

• A. $\frac{3}{10}$
• B. $\frac{9}{11}$
• C. $\frac{14}{17}$
• D. $\frac{27}{41}$

Answer 1

The correct option is D $\frac{27}{41}$

Let A = {Fair has not made a loss}
$E_1=\left\{\text{it rains}\right\},\text{then}P\left(E_1\right)=0.7$
$E_2=\left\{\text{it does not rains}\right\}\text{then}P\left(E_2\right)=0.3$

$P\left(A/E_1\right)=P$ [Fair has not made a loss on a rainy day] = 20% = 0.2
$P\left(A/E_2\right)=P$ [Fair has not made loss on non rainy day] = 90% = 0.9
By Baye's theorem,
$P\left(E_2/A\right)=\frac{P\left(E_2\right).P\left(A/E_2\right)}{P\left(E_1\right).P\left(A/E_1\right)+P\left(E_2\right).P\left(A/E_2\right)}$

$=\frac{0.3\times 0.9}{0.7\times 0.2+0.3\times 0.9}=\frac{27}{41}$