Question

you are planning a three-day trip to seattle, washington, in october. use the fact that on each day, it could either be sunny or rainy, and that each day is equally likely to be sunny or rainy to answer the following question.

what is the probability that it rains on exactly one day?

(type an integer or a decimal. do not round.)

Explanation:

Construct the sample space

Using the Sample Space Construction knowledge point

$$ S = \{SSS, SSR, SRS, SRR, RSS, RSR, RRS, RRR\} $$

$$ N(S) = 2^3 = 8 $$

Identify the favorable outcomes

Using the Sample Space Construction knowledge point

$$ E = \{SRR, RSR, RRS\} \quad \text{for exactly one sunny day} $$

$$ E = \{RSS, SRS, SSR\} \quad \text{for exactly one rainy day} $$

$$ N(E) = 3 $$

Calculate the probability

Using the Classical Probability knowledge point

$$ P(\text{exactly one rainy day}) = \frac{N(E)}{N(S)} = \frac{3}{8} = 0.375 $$

Answer:

What is the probability that it rains on exactly one day? <blank>0.375</blank>