A sample of 4 different calculators is randomly selected from a group containing 11 that are defective and 25 that have no defects. What is the probability that at least one of the calculators is defective?

To find the probability that at least one of the calculators is defective, we can first calculate the probability that none of the calculators are defective and then subtract that probability from 1. The total number of calculators in the group is 11 defective calculators + 25 non-defective calculators = 36 calculators. The probability of selecting a non-defective calculator is 25 non-defective calculators / 36 total calculators. The probability of selecting 4 non-defective calculators in a row is (25/36) * (24/35) * (23/34) * (22/33). The probability of selecting at least one defective calculator is 1 - (probability of selecting 4 non-defective calculators in a row). Let's calculate this probability. Calculate the value by following steps: - step0: Calculate: \(1-\left(\frac{25}{36}\times \frac{24}{35}\times \frac{23}{34}\left(\frac{22}{33}\right)\right)\) - step1: Reduce the fraction: \(1-\left(\frac{25}{36}\times \frac{24}{35}\times \frac{23}{34}\times \frac{2}{3}\right)\) - step2: Multiply the terms: \(1-\frac{230}{1071}\) - step3: Reduce fractions to a common denominator: \(\frac{1071}{1071}-\frac{230}{1071}\) - step4: Transform the expression: \(\frac{1071-230}{1071}\) - step5: Subtract the numbers: \(\frac{841}{1071}\) The probability that at least one of the calculators is defective is approximately 0.785 or 78.5%.