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Maya is playing a trivia game with multiple choice questions. Each question has 2 correct answers among 5 answer choices. Maya has no idea what the answers to a certain question are, so she needs to choose two different answers at random. What is the probability that Maya's first guess is CORRECT and her second guess is INCORRECT? Round your answer to two decimal places.

Maya is playing a trivia game with multiple choice questions. Each question has 22 correct answers among 55 answer choices.\newlineMaya has no idea what the answers to a certain question are, so she needs to choose two different answers at random.\newlineWhat is the probability that Maya's first guess is CORRECT and her second guess is INCORRECT?\newlineRound your answer to two decimal places.

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Q. Maya is playing a trivia game with multiple choice questions. Each question has 22 correct answers among 55 answer choices.\newlineMaya has no idea what the answers to a certain question are, so she needs to choose two different answers at random.\newlineWhat is the probability that Maya's first guess is CORRECT and her second guess is INCORRECT?\newlineRound your answer to two decimal places.
  1. Identify total answers: Identify the total number of correct answers and incorrect answers.\newlineThere are 22 correct answers and 33 incorrect answers (since there are 55 choices in total).
  2. Calculate first guess probability: Calculate the probability that Maya's first guess is correct.\newlineSince there are 22 correct answers out of 55, the probability that her first guess is correct is 25\frac{2}{5}.
  3. Calculate second guess probability: Calculate the probability that Maya's second guess is incorrect given that her first guess was correct.\newlineAfter Maya has chosen one correct answer, there is 11 correct answer and 33 incorrect answers left. The probability that her second guess is incorrect is therefore 34\frac{3}{4}.
  4. Calculate combined probability: Calculate the combined probability that Maya's first guess is correct and her second guess is incorrect.\newlineTo find the combined probability of two independent events, we multiply the probabilities of each event occurring. So, we multiply the probability of the first event (correct guess) by the probability of the second event (incorrect guess).\newlineProbability = (Probability of first guess correct) ×\times (Probability of second guess incorrect)\newlineProbability = 25\frac{2}{5} ×\times 34\frac{3}{4}
  5. Perform multiplication: Perform the multiplication to find the combined probability.\newlineProbability = (25)×(34)=620=310(\frac{2}{5}) \times (\frac{3}{4}) = \frac{6}{20} = \frac{3}{10}
  6. Convert fraction to decimal: Convert the fraction to a decimal and round to two decimal places.\newlineProbability ≈0.30\approx 0.30

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