Question

Every week, you and your three roommates draw straws to determine who cleans the bathroom and who cleans out the hamster cage. First, you and your roommates draw straws to see who has to clean the bathroom (using three short straws and one long straw). Then, you and your roommates draw straws again to see who cleans the cage. Importantly, the person who is selected to clean the bathroom is disqualified from participating in the hamster cage draw, and the number of straws are reduced accordingly. What is the likelihood that you do not have to clean the bathroom or the cage for two weeks in a row (i.e. you have no chores for two consecutive @eks)?

Answer 1

Solution

‘you and your three room mates’ => there are 4 persons.

So, probability a particular person gets assigned the first task [of bathroom cleaning] = ¼.

=> by complementary probability, P(a particular person does not get assigned the first task) = ¾

Having assigned one person for the first task, the second task [of cage cleaning] can be assigned to only one of the remaining 3 persons. So, probability a particular person gets assigned the second task [of cage cleaning] = 1/3.

=> by complementary probability, P(a particular person does not get assigned the second task) = 2/3

The above two imply that

P(a particular person is assigned neither the first task nor the second task in a week)

= (3/4) x (2/3)

= ½

And so, P(a particular person is assigned neither the first task nor the second task in two weeks)

= ½ x ½

= ¼ Answer

Done