Question:
In a box containing 100 apples, 10 are defective. The probability that in a sample of 6 apples, 3 are defective is
In a box containing 100 apples, 10 are defective. The probability that in a sample of 6 apples, 3 are defective is
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Use $P(r) = ^nC_r p^r q^{n-r}$ for sampling with a constant probability.
Updated On: Apr 26, 2026
- 0.1548
- 0.1458
- 0.01854
- 0.01458
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The Correct Option is D
Solution and Explanation
Step 1: Binomial Parameters
$n = 6$. Probability of defective apple $p = 10/100 = 0.1$.
Probability of good apple $q = 0.9$.
Step 2: Formula
$P(X=3) = ^6C_3 \cdot p^3 \cdot q^{6-3}$.
Step 3: Calculation
$20 \times (0.1)^3 \times (0.9)^3 = 20 \times 0.001 \times 0.729 = 0.02 \times 0.729 = 0.01458$.
Final Answer: (D)
$n = 6$. Probability of defective apple $p = 10/100 = 0.1$.
Probability of good apple $q = 0.9$.
Step 2: Formula
$P(X=3) = ^6C_3 \cdot p^3 \cdot q^{6-3}$.
Step 3: Calculation
$20 \times (0.1)^3 \times (0.9)^3 = 20 \times 0.001 \times 0.729 = 0.02 \times 0.729 = 0.01458$.
Final Answer: (D)
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