The half-life of a radioactive nucleus is 5 years. The fraction of the original sample that would decay in 15 years is :

Half-life = 5 years. In 15 years, number of half-lives = 15/5 = 3.

Fraction remaining after 3 half-lives: $$\left(\frac{1}{2}\right)^3 = \frac{1}{8}$$

Fraction decayed = $$1 - \frac{1}{8} = \frac{7}{8}$$

This matches option 3: $$\frac{7}{8}$$.

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