Question

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.NO SPAM OTHERWISE I WILL REPORT YOU!

a) Friends Molly and Polly have been allocated two separate rooms at the motel. What is the likely number of rooms between their rooms?

b) Molly believes there is a greater than 1/3 chance that at most one room will separate them, but Polly disagrees. Who is right? Explain why.

Answer 1

Given : A motel has ten rooms ,  all located on the same side of a single corridor and numbered 1 to 10 in numerical order.  Friends Molly and Polly have been allocated two separate rooms at the motel.

To find : the likely number of rooms between their rooms

Solution:

Moly probablty                Rooms in between  probability

Room           0         1        2      3        4       5      6       7      8          

1    (1/10)       1/9    1/9     1/9    1/9     1/9     1/9    1/9    1/9    1/9    

2   (1/10)       2/9    1/9     1/9    1/9     1/9     1/9    1/9    1/9    0    

3  (1/10)        2/9    2/9     1/9    1/9     1/9     1/9    1/9    0     0    

4  (1/10)         2/9    2/9    2/9    1/9     1/9     1/9    0     0      0      

5  (1/10)         2/9    2/9    2/9    2/9     1/9     0      0     0       0      

6  (1/10)         2/9    2/9    2/9    2/9     1/9     0      0     0       0

7  (1/10)         2/9    2/9    2/9    1/9     1/9     1/9     0      0      0

8  (1/10)         2/9    2/9     1/9    1/9     1/9     1/9    1/9    0     0      

9  (1/10)         2/9    1/9     1/9    1/9     1/9     1/9    1/9    1/9    0    

10  (1/10)        1/9    1/9     1/9    1/9     1/9     1/9    1/9    1/9    1/9    

Probability  18/90  16/90 14/90 12/90 10/90 8/90 6/90 4/90 2/90

  Likely number of rooms between their rooms

= 0 * (18/90) + 1 * (16/90) + 2(14/90) + 3(12/90) + 4(10/90) + 5(8/90) + 6(6/90)  + 7(4/90) + 8(2/90)

=  (1/90)(0 + 16 + 28 + 36 + 40 + 40 + 36 + 28 + 16)

= 240/90

=24/9

= 8/3

= 2.33 rooms

likely number of rooms between their rooms = 2.33

At most 1 room = 0 room or 1 room

= (18 + 16)/90

= 34/90

34/ 90 > 30/90

=> 34/90 > 1/3

=> Moly belief is right that    there is a greater than 1/3 chance that at most one room will separate them          

Learn more:

In a Family of 3 children find probability of having at least one boy ...

https://brainly.in/question/7700718

consider a random experiment in which a coin is tossed and if the ...

https://brainly.in/question/8846982

Find the probability distribution of the numbers obtained in throwing ...

https://brainly.in/question/13162018