A bag holds 3 red and 2 blue marbles. Two are drawn without replacement. Given that the second marble is red, what is the probability that the first was also red?
Answer and explanation
Correct answer: A. 1/2
- Step 1: Find P(second is red): P(RR) + P(BR) = (3/5)(2/4) + (2/5)(3/4) = 3/10 + 3/10 = 3/5.
- Step 2: The joint event 'first red and second red' has probability (3/5)(2/4) = 3/10.
- Step 3: Conditional probability: (3/10) / (3/5) = 1/2.
Answer
1/2.
Why not the others: '3/5' is the unconditional chance of a red marble; '2/5' is the chance of a blue first draw; '3/10' is the joint probability and was not divided by P(second red).
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