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On average 15% of tomatoes are defective. In a batch of 20, the binomial probability of exactly 3 defective tomatoes is:
A0.2428
B0.0415
C0.2240
D0.1762
Answer & Solution
Correct answer: A. 0.2428
1. Use $P(X=x)=\binom{n}{x}p^{x}q^{n-x}$ with $n=20$, $p=0.15$, $q=0.85$.
2. $\binom{20}{3}=1140$.
3. $P(X=3)=1140\times(0.15)^3\times(0.85)^{17}$.
4. This evaluates to $0.2428$.
5. $0.0415$ comes from substituting $n=6$ instead of $n=20$; $0.2240$ is the Poisson value for the same count.
_Source: NECTA ACSEE 2023 Advanced Mathematics 142/2, Question 1: Probability_
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