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

$\frac{7}{13}$

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

$=P\left(E_2 / A\right)=\frac{P\left(E_2 \cap A\right)}{P(A)}$

$=\frac{P\left(E_2\right) . P\left(A / E_2\right)}{P(A)}$

$=\frac{\frac{7}{10} . \frac{3}{10}}{\frac{39}{100}}=\frac{7}{13}$