A certain type of battery has a 0.5% failure rate. Find the probability that a shipment of 1,000 batteries has more than two defective batteries.
A) 0.175
B) 0.125
C) 0.875
D) 0.600

Question

Quizplus · Accepted Answer

The probability of having more than two defective batteries can be found by subtracting the probability of having two or fewer defective batteries from 1. The probability of exactly k defects in n trials (with the probability of defect p) follows a binomial distribution: P(X=k) = (n choose k) * p^k * (1-p)^(n-k). Here, n=1000, p=0.005, and we're interested in the complement of P(X ≤ 2). Calculating P(X=0), P(X=1), and P(X=2) and summing them gives the probability of two or fewer defects. Subtracting this sum from 1 gives the probability of more than two defects. This approach, while conceptually correct, involves cumbersome calculations directly but is simplified by recognizing it as a common type of problem where the complement rule is easier to apply. The exact numbers would typically require computational tools due to the large factorial values in binomial coefficients. The answer is approximated based on the understanding that the likelihood of having more than two defective batteries is relatively high given the large sample size and the non-negligible defect rate.

A Certain Type of Battery Has a 0