SOLUTION: A real estate agent has 8 master keys to open several new homes. only 1 master key will open any given house. if 40% of these homes are usually left unlocked, what is the probabili

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Question 938671: A real estate agent has 8 master keys to open several new homes. only 1 master key will open any given house. if 40% of these homes are usually left unlocked, what is the probability that the real estate agent can get into a specific home if the agent selects 3 master keys at random before leaving the office?
Answer by mathmate(429) About Me  (Show Source):
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Given:
- 8 master keys, only one can open each home.
- 40% of the homes are unlocked.
- agent took 3 of the 8 master keys with him

Solution:
Since 40% of the homes are unlocked, only 60% of the homes need a master key, of which there is a probability of 3/8 of opening by the master keys.
Overall probability
P(opening door) = 0.40+%2B+0.60%283%2F8%29 = 0.40 + 0.225 = 0.625 = 5%2F8
Answer: there is a probability of 5%2F8 that the agent can get in a specific home