🎈 Example with Replacement: Drawing Balls from an Urn
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Question:
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An urn contains 3 red and 5 blue balls. Two balls are drawn in succession with replacement. What is the probability of drawing a red ball twice?
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Step-by-step Solution:
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- Probability for a red ball per draw: \(\frac{3}{8}\)
- Because drawing is with replacement, the probability remains the same.
- For two reds: \(P = \frac{3}{8} \times \frac{3}{8} = \frac{9}{64}\)
- Decimal value: ≈ 0.1406
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Answer:
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The probability of drawing a red ball twice in succession with replacement is \( \frac{9}{64} \) or about 14.1%.
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