<p>The probability that an event \(A\) happens in one trial of an experiment is 0.4. Three independent trials of the experiment are performed. The probability that the event \(A\) happens at least once is</p>
Step-by-Step Solution
Key Concept: Use the complement approach: P(at least once) = 1 - P(never happens). For independent trials, P(never) = (1-p)^n where p is the probability in one trial.
<p><strong>Step 1:</strong> Identify that we need P(A happens at least once in 3 trials).</p><p><strong>Step 2:</strong> Use complement: P(at least once) = 1 - P(never happens in any trial).</p><p><strong>Step 3:</strong> Probability of A not happening in one trial = 1 - 0.4 = 0.6.</p><p><strong>Step 4:</strong> For 3 independent trials, probability A never happens = (0.6)³ = 0.216.</p><p><strong>Step 5:</strong> Therefore, P(A happens at least once) = 1 - 0.216 = 0.784.</p><p><strong>Alternatively:</strong> 0.784 = 784/1000 = 98/125 (if options are in fraction form).</p><p>∴ Answer: B</p>
Correct Answer: B