SOLUTION: I have a question from Statistics. Please explain the solution. Here is the problem: A key ring contains 4 office keys that are identical in appearance, but only one will open your

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Question 915320: I have a question from Statistics. Please explain the solution. Here is the problem: A key ring contains 4 office keys that are identical in appearance, but only one will open your office door. Suppose you randomly select one key and try it. If it does not fit, you randomly select one of the three remaining keys. If it does not fit, you randomly select one of the last two. Each different sequence that could occur in selecting the keys represents one of a set of equiprobable simple events.
a) List the simple events in S and assign probabilities to the simple events.
b) Let x equal the number of keys that you try before the one that opens the door (x= 1, 2, 3, 4). Then assign the appropriate value of x to each simple event.
c) Calculate the values of p(x) and display them in a table.
d) Construct a probability histogram for p(x)
Answer by Fombitz(32388) (Show Source):
You can put this solution on YOUR website!
Let A be the key that is correct.
Look at all the possible choices determine x for each.
A B C D 1
A B D C 1
A C B D 1
A C D B 1
A D B C 1
A D C B 1
B A C D 2
B A D C 2
B C A D 3
B C D A 4
B D A C 3
B D C A 4
C A B D 2
C A D B 2
C B A D 3
C B D A 4
C D A B 3
C D B A 4
D A B C 2
D A C B 2
D B A C 3
D B C A 4
D C A B 3
D C B A 4
Each event is equally likely and there are 24 possible outcomes.

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