AnswersProbability and Statistics with Applications Honors Sem-2-FL-1210300 2024-2025Geometric Random VariablesQuestion 163897
163897
AssignmentMultiple Choice

Geometric Random Variables

Question 163897 • Probability and Statistics with Applications Honors Sem-2-FL-1210300 (2024-2025)

Eighteen percent of apples grown in an orchard have defects. Let X = the number of apples that are randomly inspected from the orchard until a defective one is found.What is the probability that the first defective apple found is the 10th one inspected?Round to 2 decimal places.

Answer
A
0
B
0.03
C
0.14
D
0.86

Explanation

For the first defective apple to be the 10th inspected, the first 9 apples must be nondefective and the 10th must be defective. The probability is 0.82⁹ × 0.18 ≈ 0.0302, which rounds to 0.03. The correct choice is B, 0.03.

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