To solve this problem, we need to determine the probability that John hits either the Bull's eye or the 10-point ring.
Step-by-step solution:
1. Determine the probability of hitting the Bull's eye:
- The probability that John hits the Bull's eye is given as [tex]\( \frac{1}{10} \)[/tex].
2. Determine the probability of hitting the 10-point ring:
- The probability that John hits the 10-point ring is given as [tex]\( \frac{3}{10} \)[/tex].
3. Calculate the probability of hitting either the Bull's eye or the 10-point ring:
- Hitting the Bull's eye and hitting the 10-point ring are mutually exclusive events (they cannot happen at the same time).
- When events are mutually exclusive, the probability of either event occurring is the sum of their individual probabilities.
Thus, the probability that John either hits the Bull's eye or the 10-point ring is:
[tex]\[
\frac{1}{10} + \frac{3}{10} = \frac{1 + 3}{10} = \frac{4}{10} = 0.4
\][/tex]
4. Convert the probability to the fraction form:
- The numerical value 0.4 can be expressed as the fraction [tex]\( \frac{4}{10} \)[/tex], which simplifies to [tex]\( \frac{2}{5} \)[/tex].
Based on the calculations, the correct answer is:
[tex]\[
\boxed{\frac{2}{5}}
\][/tex]
