A bag contains 3 red and 2 blue balls. If you draw two balls with replacement, what is the probability both are red?

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Prepare for the AMSOC 26-003 Module A Test. Utilize flashcards and multiple choice questions with hints and explanations. Ace your exam!

Multiple Choice

A bag contains 3 red and 2 blue balls. If you draw two balls with replacement, what is the probability both are red?

Explanation:
Drawing with replacement keeps the bag composition the same for each draw, so the two draws are independent. The chance of red on one draw is 3 out of 5, and because the ball is replaced, the chance on the second draw is still 3 out of 5. Multiply the probabilities: (3/5) × (3/5) = 9/25. So the probability both draws are red is 9/25. (If you were not replacing the ball, the second draw would have a different probability, giving 3/10, which is a different scenario.)

Drawing with replacement keeps the bag composition the same for each draw, so the two draws are independent. The chance of red on one draw is 3 out of 5, and because the ball is replaced, the chance on the second draw is still 3 out of 5. Multiply the probabilities: (3/5) × (3/5) = 9/25. So the probability both draws are red is 9/25. (If you were not replacing the ball, the second draw would have a different probability, giving 3/10, which is a different scenario.)

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