Question:
The probability that event A happens in a trial is 0.4. If three independent trials are made, then the probability that A happens at least once is.......
The probability that event A happens in a trial is 0.4. If three independent trials are made, then the probability that A happens at least once is.......
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Use the complement: 1 minus the probability that it never happens.
Updated On: Oct 1, 2026
- \(0.216\)
- \(0.926\)
- \(0.064\)
- \(0.784\)
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the Concept
"At least once" is the complement of "never". Since the trials are independent, the probability of never is the product of the failure probabilities.
Step 2: Compute
\(P(\text{A fails in one trial}) = 1 - 0.4 = 0.6\).
\[ P(\text{never}) = 0.6^3 = 0.216 \]
\[ P(\text{at least once}) = 1 - 0.216 = 0.784 \]
Option (A), 0.216, is the probability of never, and (C), 0.064, is the probability of three successes.
Final Answer:
The probability is 0.784, option (D). \[ \boxed{0.784} \]
"At least once" is the complement of "never". Since the trials are independent, the probability of never is the product of the failure probabilities.
Step 2: Compute
\(P(\text{A fails in one trial}) = 1 - 0.4 = 0.6\).
\[ P(\text{never}) = 0.6^3 = 0.216 \]
\[ P(\text{at least once}) = 1 - 0.216 = 0.784 \]
Option (A), 0.216, is the probability of never, and (C), 0.064, is the probability of three successes.
Final Answer:
The probability is 0.784, option (D). \[ \boxed{0.784} \]
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