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Home » Try $\theta = \frac\pi4$: - RoadRUNNER Motorcycle Touring & Travel Magazine

Try $\theta = \frac\pi4$: - RoadRUNNER Motorcycle Touring & Travel Magazine

📅 April 30, 2026 👤 scraface

Apr 30, 2026

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📌 $$Question: A statistician developing new methods for analyzing social networks observes that two individuals, Alice and Bob, independently choose a random time between 1:00 PM and 2:00 PM to send a message. Given that Alice sends her message after Bob, what is the probability that Bob sent his message before 1:30 PM?

📌 Solution: We are given that Alice and Bob each choose a uniform random time between 1:00 PM and 2:00 PM to send a message, and we are given the condition that Alice sends after Bob. We are to compute the conditional probability that Bob sent his message before 1:30 PM, given this information.

📌 Thus, the probability that Bob sent his message before 1:30 PM, given that Alice sent after him, is $

📌 Question: A science fair judge evaluates a project where a student rolls four fair 6-sided dice, each labeled from 1 to 6. What is the probability that exactly two of the dice show a number greater than 4?

📌 Solution: We are to compute the probability that exactly two out of four fair 6-sided dice show a number greater than 4.

📌 Each die has numbers 1 through 6. The probability that a single die shows a number greater than 4 is:

📌 The probability that a die shows a number 4 or less is:

📌 Question: A science fair judge reviews a project involving word puzzles. The project involves arranging the letters of the word MATHEMATICS to form distinct permutations. How many such distinct permutations exist?

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