A motel has ten rooms, all located on the same side of a single corridor and numbered 1 to 10 in numerical order. The motel always randomly allocates rooms to its guests, There are no other guests besides those mentioned.
A.) Friends Molly and Polly have been allocated two separate rooms at the motel. What is the most likely number of rooms between their rooms?
B.) Molly believes there is a greater than one-third chance that at most one room will seperate them, but Polly disagrees. Who is right? Explain why.
C.) On another occasion, Molly, Polly, and a third friend, Ollie, were allocated three seperate rooms. Molly believes there is a better than one-third chance they are all within a block of five consecutive rooms. Ollie believes there is exactly one-third chance and Polly believes there is less than one-third chance. Who is right? Explain why.
D.) Ollie has arrived after rooms were allocated to Molly and Polly. There was then a 50% chance he would be in a room adjacent to Molly or Polly or both. In how many ways could a pair of rooms have been allocated to Molly and Polly.
Answers
Answer:
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