A real estate man has eight master keys to open several new houses. Only one master key will open a given house. If 40% of these houses are usually unlocked,the probability that the real estate man can get into a specific house,if he selects three master keys at random,is?
My approach: Let the 3 keys (A,B and C) have selected among 8 keys with each having probability 1/8.
If key A has successfully unlocked then there is no need to unlock the house by B and C .
If key A become unsuccessful but by key B if house is Unlocked then there is no need to unlock by key C.
If key A and B have unsuccessful then by key C we can unlocked the house.
P(get into house by three key)= (4/10) + (6/10)(1/8) + (6/10)(7/8)(1/8) + (6/10)(7/8)(7/8)(1/8).
Is my approach correct?