A student claims that if the odds in favor of winning a game are a:b, then out of every a+b games she would win a games. Hence, the probability of the event of winning the game is a/b+b Is the student's reasoning correct? why or why not?
Typos? Odds of winning = a/(a+b) = # winning games over total.
The student's reasoning is not correct. The probability of winning a game is not equal to a/b + b.
To understand why this is incorrect, let's clarify a few terms. The odds in favor of winning a game are typically expressed as a ratio a:b. This means that out of every a+b games, the player wins a games and loses b games.
However, the probability of winning a game is defined as the number of favorable outcomes divided by the total number of possible outcomes. In this case, the number of favorable outcomes would be a (the number of games won), and the total number of possible outcomes would be a+b (the total number of games played).
Therefore, the correct probability of winning the game can be expressed as P(win) = a / (a + b).
To summarize, the student's reasoning is incorrect because adding a/b and b together does not represent the probability of winning the game. The correct probability is a / (a + b), which measures the success rate of winning a game out of all the possible outcomes.