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3. (2 marks) A real estate agent has 8 keycards to open new model homes. Only one keycard will open any specific model home. 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 chooses 3 keycards at random before leaving the office

Respuesta :

Answer:

0.625

Step-by-step explanation:

We are told that the agent has 8 keycards.

We are also told that only one of the keycards can open each home.

Now, if the agent took 3 out of the 8 keycards with him, it means that;

Probability of opening by the keycards = ⅜

We are told that 40% or 0.4 of these homes were left unlocked.

This means that 60% or 0.6 are those that will require a key card.

Thus, probability of agent getting into a specific home is;

P(agent getting into a specific home) = 0.4 + 0.6(⅜)

P(agent getting into a specific home) = 0.4 + 0.6(0.375) = 0.625

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