We are given a list of weekly chores from which Ryan randomly choose a chore he must complete.
Weekly Chores
Collecting the trash
Folding the laundry
Cleaning the house
Washing the dishes
Cutting the grass
Now, we know that the first week Ryan chose washing the dishes. Note that the outcomes of the choices are not related so these choices are independent events. This means that the probability that Ryan will choose washing the dishes two more weeks in a row is the product of the probabilities of choosing this chore.
P(both weeks washing the dishes) = P(washing the dishes)* P(washing the dishes)
The probability of washing the dishes is equal in every week because the results of choices are independent. Because washing the dishes is 1 out of 5 possible chores, the probability of choosing washing the dishes is 1 5.
P(both weeks washing the dishes)=1/5* 2/5
Let's evaluate the probability!
