Question

You are planning a three-day trip to Seattle, Washington in October. List the sunny day/rainy day sample space. List the outcome(s) of event "It rains on exactly one day." List the outcome(s) of event "It rains on at least one day."

a) Sunny, Rainy, Rainy
b) Sunny, Sunny, Rainy
c) Rainy, Rainy, Rainy
d) Sunny, Sunny, Sunny

Answer 1

The question involves the probability of different weather outcomes over a three-day period in Seattle. An eight-outcome sample space is described, and the outcomes for both 'it rains on exactly one day' and 'it rains on at least one day' are listed.

Step-by-step explanation:

The subject of this question is mathematics, specifically probability and statistics which are part of the high school curriculum. The question involves determining different potential weather outcomes (sunny or rainy) over a three-day period, and listing the appropriate sample space and specific event outcomes.

For the sunny day/rainy day sample space, we have these combinations over the three days:

• Sunny, Sunny, Sunny
• Sunny, Sunny, Rainy
• Sunny, Rainy, Sunny
• Sunny, Rainy, Rainy
• Rainy, Sunny, Sunny
• Rainy, Sunny, Rainy
• Rainy, Rainy, Sunny
• Rainy, Rainy, Rainy

The outcomes for the event "It rains on exactly one day" are:

• Sunny, Sunny, Rainy
• Sunny, Rainy, Sunny
• Rainy, Sunny, Sunny

The outcomes for the event "It rains on at least one day" encompass all possible combinations except Sunny, Sunny, Sunny. Hence, the following outcomes are included:

• Sunny, Sunny, Rainy
• Sunny, Rainy, Sunny
• Sunny, Rainy, Rainy
• Rainy, Sunny, Sunny
• Rainy, Sunny, Rainy
• Rainy, Rainy, Sunny
• Rainy, Rainy, Rainy