Question:
Three numbers are chosen from 1 to 30. The probability that minimum is 10 and maximum is 26 is _______
Three numbers are chosen from 1 to 30. The probability that minimum is 10 and maximum is 26 is _______
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Use the complement: 1 minus the probability that it never happens.
Updated On: Oct 1, 2026
- \(\frac{1}{406}\)
- \(\frac{3}{812}\)
- \(\frac{5}{812}\)
- \(\frac{7}{812}\)
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept:
\(P(A) = 0.4\), so \(P(\text{not }A) = 0.6\). The trials are independent.
Step 2: Complement:
The probability that A never happens in three trials is \(0.6^3 = 0.216\).
Step 3: At least once:
\[ P = 1 - 0.216 = 0.784 \]
The value 0.216 in option (A) is only the probability of no occurrence, so it is not the answer.
Final Answer:
The probability is 0.784, option (D). \[ \boxed{0.784} \]
\(P(A) = 0.4\), so \(P(\text{not }A) = 0.6\). The trials are independent.
Step 2: Complement:
The probability that A never happens in three trials is \(0.6^3 = 0.216\).
Step 3: At least once:
\[ P = 1 - 0.216 = 0.784 \]
The value 0.216 in option (A) is only the probability of no occurrence, so it is not the answer.
Final Answer:
The probability is 0.784, option (D). \[ \boxed{0.784} \]
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