Rain Or Shine

The weather during the Smedleys' vacation was strange.

It was cloudy on 13 different days,

but it was never cloudy for an entire day.

Cloudy mornings were followed by clear afternoons.

Cloudy afternoons were preceded by clear mornings.

There were 11 clear mornings and 12 clear afternoons in all.

Utilize the above information to solve the following problems.

Problem 1: Produce a graph which represents all of the possible combinations of mornings and afternoons.

Problem 2: From the information given, determine how many days each of the combinations occurred. Determine the number of days the morning weather occurs, and then the number of days the afternoon weather occurs based on the morning weather. For example, determine the number of days the mornings were cloudy and then the number of days the afternoons were cloudy if the mornings were cloudy.

Problem 3: Determine how long the vacation was from the information given in your graph.

Problem 4: Based on the information given and the graph you have produced, determine the probabilities of each possible outcome occurring. For example, determine the probability of the morning weather being cloudy, and then the probability the afternoon weather being cloudy.

Problem 5: What is the probability of a cloudy day for an entire day?

Problem 6: What is the probability of a clear afternoon after a clear morning?

Problem 7: What is the probability of a cloudy afternoon after a clear morning?

Problem 8: What is the probability of a cloudy morning preceding a cloudy afternoon?