Math Problem Statement
Solution
To solve this problem, we need to find the probability that a five-day school week contains at least one snow day, given that the probability of a snow day on any given day is .
Step-by-step solution:
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Define the given probabilities:
- The probability that a snow day does happen on a given day is .
- The probability that a snow day does not happen on a given day is .
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Find the probability of no snow day in a 5-day week: We want to calculate the probability that there are no snow days in the entire five-day week. Since the events are independent, we multiply the probabilities of no snow day for each of the five days:
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Find the probability of at least one snow day: The probability of at least one snow day is the complement of the probability of no snow days. That is:
So, the probability that there is at least one snow day in a five-day school week is , or approximately 0.7627 (about 76.27%).
Would you like more details or further explanations?
Here are five related questions to expand on this topic:
- What is the probability of exactly one snow day in a five-day week?
- How would the result change if the probability of a snow day were instead of ?
- What is the probability of having snow on all five days?
- How would you compute the expected number of snow days in a week?
- How does this problem relate to binomial probability distribution?
Tip: When dealing with "at least one" problems, it's often easier to compute the complement (no occurrences) and subtract it from 1!
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Math Problem Analysis
Mathematical Concepts
Probability
Complement Rule
Independent Events
Formulas
P(no snow day) = 1 - P(snow day) = 3/4
P(no snow days in 5 days) = (3/4)^5
P(at least one snow day) = 1 - P(no snow days in 5 days)
Theorems
Complement Rule
Probability of Independent Events
Suitable Grade Level
Grades 9-12
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