A real estate man has eight master keys to open several new homes. Only one master key will open any given home. If 40% of these homes are usually left unlocked, the probability that the real estate man can get into a specific home, if it is given that he selected 3 keys randomly before leaving his office, is equal to

$\frac{5}{8}$

E₁ : Specific home is locked.

E₂ : Specific home is unlocked.

A : Real estate man get in to the home.

$P\left(E_2\right)=\frac{40}{100}=\frac{2}{5}, P\left(E_1\right)=\frac{3}{5}$

$P(A)=P\left(E_1\right) . P\left(A / E_1\right)+P\left(E_2\right) . P\left(A / E_2\right)$

$=\frac{3}{5} . \frac{{ }^7 C_2}{{ }^8 C_3}+\frac{2}{5} . 1$

$=\frac{25}{40}=\frac{5}{8}$