The probability that an archer hits the target when it is windy is equal to 2/5, when it is not windy his probability of hitting the target is 7/10. On any shot the probability of gust of wind is $\frac{3}{10}$. The probability that there is no gust of wind on the occasion when he missed the target, is equal to
Answer & explanation
Correct answer: option 3
E1 : There is a gust of wind.
E2 : There is no gust of wind.
A : archer misses the target.
P(A) = P(E1) . P(A / E1) + P(E2) . P(A / 2E2)
$=\frac{3}{10} . \frac{3}{5}+\frac{7}{10} . \frac{3}{10}$
$=\frac{39}{100}$
Now, required probability
$=P\left(E_2 / A\right)=\frac{P\left(E_2 \cap A\right)}{P(A)}$
$=\frac{P\left(E_2\right) . P\left(A / E_2\right)}{P(A)}$
$=\frac{\frac{7}{10} . \frac{3}{10}}{\frac{39}{100}}=\frac{7}{13}$