SOLUTION: I have five identical keys on a ring two of which will open the door what is the probability that i will get door open on the first or second try.

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Question 305012: I have five identical keys on a ring two of which will open the door what is the probability that i will get door open on the first or second try.
Found 2 solutions by richwmiller, MathTherapy:
Answer by richwmiller(9135) About Me  (Show Source):
You can put this solution on YOUR website!
There is a difficulty with the problem as written.
If the keys are identical then all the keys are the same and will open the door.
Let's assume that they only appear identical.
2/5 for the first key and 2/4 for the second key
4/10+5/10=9/10
that seems very high

Answer by MathTherapy(1421) About Me  (Show Source):
You can put this solution on YOUR website!
I have five identical keys on a ring two of which will open the door what is the probability that i will get door open on the first or second try.

The keys cannot be identical because if they are, anyone can close their eyes and any chosen key would open the door. It's apparent that they MAY appear identical.

In that case, using A and B as the correct keys, the probability of choosing A or B, or P(A or B) = P(A) + P(B)

Now this calculation is dependent on whether or not you return each key to the bunch after trying each one. If not, then we get:

P(A) + P(B) = 2%2F5 + 1%2F4 = highlight_green%2813%2F20%29

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