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The problem involves calculating the probability that all three shots fired by a shooter hit the target, given the probability \( p = 0.9 \) of hitting the target with a single shot. The solution is as follows:

### Solution:
If the probability of hitting the target on a single shot is \( p = 0.9 \), then the probability of hitting the target on all three shots is calculated by multiplying the probabilities of success for each shot:

\[
P(\text{all three hits}) = p \cdot p \cdot p = p^3
\]

Substituting \( p = 0.9 \):

\[
P(\text{all three hits}) = 0.9^3 = 0.729
\]

### Final Answer:
The probability that all three shots hit the target is:

\[
\boxed{0.729}
\]

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Would you like further details on this problem or related concepts? 

Here are 5 related questions you might find interesting:
1. What is the probability that at least one shot misses the target?
2. If the shooter takes 5 shots, what is the probability that all 5 hit the target?
3. How does the probability change if the hit probability \( p \) is reduced to \( 0.8 \)?
4. What is the expected number of hits out of 3 shots, given \( p = 0.9 \)?
5. How would you model this situation if the number of shots were a random variable?

**Tip:** For situations involving independent events, probabilities are multiplied to determine joint outcomes.

The probability of hitting the target with a single shot is p = 0.9. The shooter fired 3 shots. Find the probability that all shots hit the target.

Learn how to calculate the probability that all three shots fired by a shooter hit the target, given the hit probability p = 0.9 per shot. Includes step-by-step calculation for Grades 9-12 students.

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