  # You are planning a 3 day trip to Seattle. Each day could be sunny or rainy.Each day is equally likely to be suny or rainy. What is the portability that it rains on exactly one day?  How do I set this tupe of problem up. What is the number for event E? Sample Space?

Question

You are planning a 3 day trip to Seattle. Each day could be sunny or rainy.Each day is equally likely to be suny or rainy. What is the portability that it rains on exactly one day?  How do I set this tupe of problem up. What is the number for event E? Sample Space?

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Step 1

Equally likely probabilities:

The total probability of all possible outcomes is always 1.

Now, there are two possible outcomes for each day- sunny and rainy, which are equally likely, that is, equally probable. This means, one a particular day, the two events have the same probability of occurrence.

Denote the event that a day is sunny as “S” and that the day is rainy as “R”.

Since total probability is 1, P (S) + P (R) = 1.

Since it is equally likely for a day to be sunny and rainy, P (S) = P (R) = p (suppose).

Therefore, P (S) + P (R) = 1 implies that:

p + p = 2p = 1.

So, p = 1/2 = 0.5.

Thus, P (S) = P (R) = 0.5.

Step 2

Sample space:

Sample space is the collection of all possible outcomes.

Here, there are 3 days. Each day can either be an S (sunny) or an R (rainy). Keeping this in mind, a sequence of length 3 can be formed with these letters, depending upon whether the day is sunny or rainy, with the first position in the sequence denoting the first day, the second position denoting the second day, an...

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### Basic Probability 