Answer:
The probability for part one is 1/8.
For part two, the probability is 7/8.
Step-by-step explanation:
We designate 's' to signify a sunny day and 'r' to denote a rainy day. For example, (s,s,s) means all three days are sunny, while (s,r,s) indicates sunny, rainy, then sunny.
Collecting all possible daily weather outcomes over three days provides the sample space Ω = {(s,s,s), (r,s,s), (s,r,s), (s,s,r), (s,r,r), (r,s,r), (r,r,s), (r,r,r)}. This set contains 8 equally likely events since the chance of rain equals the chance of sun each day.
The probability of any specific event equals the count of favorable cases divided by the total in Ω, which is 8.
Part one: Only (s,s,s) fits the condition of all sunny days, so its probability is 1 divided by 8.
Part two: The favorable outcomes are all events with at least one rainy day, meaning every event except (s,s,s), totaling 7 cases. The resulting probability is 7/8.
An alternate way to find part two’s answer is recognizing it as the complement of all sunny days. Since the latter is 1/8, subtracting this from 1 yields 7/8.
Hope this explanation clarifies your doubts!
