Math Problem Statement
The probability of winning a particular game is 3/5. (Assume all games are independent) Given that, when the game is played m times, the probability of winning exactly two games is three times the probability of winning exactly one game, find the value of m.
Solution
To solve this problem, we can use the binomial probability formula. The probability of winning a game is given as (
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Math Problem Analysis
Mathematical Concepts
Probability
Binomial Distribution
Combinatorics
Formulas
Binomial probability formula: P(X = k) = C(m, k) * p^k * (1-p)^(m-k)
Theorems
Binomial Theorem
Independent events probability
Suitable Grade Level
Grades 10-12
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