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QuestionIn the 2023 US Open, 128 players compete in Women's Singles, with 24 being American. What is the probability an American wins? Answer as a fraction or %\% (rounded to the nearest tenth, e.g., 10.6%10.6\%).

Studdy Solution

STEP 1

Assumptions1. The total number of players is128. The number of American players is243. Every player is equally likely to win the tournament

STEP 2

The probability of an event is calculated by dividing the number of favorable outcomes by the total number of outcomes. In this case, the favorable outcome is an American player winning, and the total outcomes are the total number of players.
Probability=Number of favorable outcomesTotal number of outcomesProbability = \frac{Number\, of\, favorable\, outcomes}{Total\, number\, of\, outcomes}

STEP 3

Now, plug in the given values for the number of favorable outcomes (American players) and the total number of outcomes (total players) to calculate the probability.
Probability=24128Probability = \frac{24}{128}

STEP 4

implify the fraction to its lowest terms.
Probability=316Probability = \frac{3}{16}

STEP 5

To convert this probability to a percentage, multiply the fraction by100.
Probability (%)=Probability×100Probability\, (\%) = Probability \times100

STEP 6

Now, plug in the given value for the probability to calculate the percentage.
Probability (%)=316×100Probability\, (\%) = \frac{3}{16} \times100

STEP 7

Calculate the percentage and round to the nearest tenth of a percent.
Probability (%)=316×100=18.75%Probability\, (\%) = \frac{3}{16} \times100 =18.75\%The probability that an American player will win the tournament this year is 316\frac{3}{16} or approximately 18.%18.\%.

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