Math Problem Statement
Two fair dice are thrown and the number showing on each is noted. Find the probability that: the sum of the number is less than or equal to 7. at least one dice shows a 3. at least one dice shows a 3, given that the sum is less than 8.
Solution
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Math Problem Analysis
Mathematical Concepts
Probability Theory
Conditional Probability
Formulas
Total number of outcomes for two dice = 6 × 6 = 36
Probability of an event = (Number of favorable outcomes) / (Total number of outcomes)
Conditional Probability P(A|B) = P(A ∩ B) / P(B)
Theorems
Basic Probability
Conditional Probability Theorem
Suitable Grade Level
Grades 9-11