4.90 Which Key Fits? A key ring contains four office keys that are identical in appearance, but only one will open your office door. Suppose you ran- domly 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 you find 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).