N Question 19, 9.3.A-14 If the odds against Deborah's winning first prize in a chess tournament are 4 to 5 , what is the probability of the event that she will win first prize? The probability that Deborah will win first place is \( \square \). (Type an integer or a fraction.) Th of 30 points

To find the probability of Deborah winning first prize given the odds against her are 4 to 5, you first need to understand that "odds against" means for every 4 times she doesn’t win, she wins 5 times. To convert odds into probability, use the formula: Probability = Wins / (Wins + Losses) Here, Wins = 5 and Losses = 4. So, the probability that Deborah will win first place is \( \frac{5}{4 + 5} = \frac{5}{9} \). Now, let's take a spin through chess history! Did you know that chess tournaments have been around since at least the 15th century? The very first recorded tournament took place in London in 1851, organized by chess master Howard Staunton. It sparked a whole new interest in competitive chess, paving the way for modern tournaments seen today—like the one Deborah is competing in! When it comes to probabilities, remember to pay attention to the wording! A common mistake is to confuse "odds against" with "probability," leading to errors in calculations. Always clarify what the odds represent and ensure you set up your fractions accurately before jumping into final calculations. Double-checking your work can help avoid those sneaky errors!