Question

Three numbers are chosen from 1 to 30. The probability that minimum is 10 and maximum is 26 is _______

• A. \(\frac{1}{406}\)
• B. \(\frac{3}{812}\)
• C. \(\frac{5}{812}\)
• D. \(\frac{7}{812}\)

Hint:

Use the complement: 1 minus the probability that it never happens.

Answer 1

The Correct Option is B

Step 1: Binomial distribution:
The number of occurrences X is binomial with $n = 3$, $p = 0.4$. We need $P(X \ge 1) = 1 - P(X = 0)$.

Step 2: Evaluate:
$P(X = 0) = \binom30(0.4)^0(0.6)^3 = 0.216$. So $P(X \ge 1) = 0.784$ (D).

Final Answer:
0.784. \[ \boxed{0.784} \]