A bag contains 3 red and 2 blue balls. If you draw two balls without 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 without replacement, what is the probability both are red?

Explanation:
Think of drawing two balls in order without putting the first back. The chance the first ball is red is 3 out of 5. If that happens, there are now 2 red balls left out of 4 total, so the second ball is red with probability 2/4 = 1/2. Multiply the two steps: (3/5) * (1/2) = 3/10. An equivalent way is to count favorable pairs: choose 2 red from 3 and two balls from 5, which gives C(3,2)/C(5,2) = 3/10. So the probability is 3/10.

Think of drawing two balls in order without putting the first back. The chance the first ball is red is 3 out of 5. If that happens, there are now 2 red balls left out of 4 total, so the second ball is red with probability 2/4 = 1/2. Multiply the two steps: (3/5) * (1/2) = 3/10. An equivalent way is to count favorable pairs: choose 2 red from 3 and two balls from 5, which gives C(3,2)/C(5,2) = 3/10. So the probability is 3/10.

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