Correct Answer: Option C

Explanation

To find the probability that two beads drawn (with replacement) are of the same color, we consider two cases: both red and both white.

 Beads = 5, White beads = 7, Total beads = 12

Both Red:
\(P(\text{Red}) = \frac{5}{12}, \quad P(\text{Both Red}) = \frac{5}{12} \times \frac{5}{12} = \frac{25}{144}\)

Both White:
\(P(\text{White}) = \frac{7}{12}, \quad P(\text{Both White}) = \frac{7}{12} \times \frac{7}{12} = \frac{49}{144}\)

Total Probability of Same Color:
\(P(\text{Same Color}) = \frac{25}{144} + \frac{49}{144} = \frac{74}{144} = \frac{37}{72}\)

The probability that the two beads are the same color is \( \frac{37}{72}\).

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