Target practice with hit probability 0.3 per shot and 10 shots. What is the probability of at least one hit?

Introduction / Context:
With independent trials, the probability of “at least one success” is one minus the probability of “no success at all.” Here, success = hit, p = 0.3 per shot, n = 10 shots.

Given Data / Assumptions:

• Per-shot hit probability p = 0.3, miss probability q = 0.7.
• Number of shots n = 10 (independent).

Concept / Approach:
P(≥1 hit) = 1 − P(0 hits) = 1 − q^n with q = 0.7.

Step-by-Step Solution:
P(0 hits) = (0.7)^{10}.Therefore P(≥1 hit) = 1 − (0.7)^{10}.

Verification / Alternative check:
As p increases or n grows, the probability approaches 1, consistent with intuition.

Why Other Options Are Wrong:
(0.7)^10 is the probability of zero hits; (0.3)^10 is “all hits” if inverted (actually all-hit probability is (0.3)^{10}); 1 is only true in the limit, not exactly; 1 − (0.3)^10 is not the correct complement.

Common Pitfalls:
Confusing “at least one” with “exactly one,” or complementing the wrong event.

Final Answer:
1 - (0.7)^10