CA Foundation · Quantitative Aptitude · Theoretical Distributions
A quality inspector at a Surat factory tests 5 independently made items, each with a 0.4 chance of being defective. What is the probability that at least one item is defective?
The probability is 0.92224. Having at least one defective item is the complement of having none. The chance that none is defective is 0.6 raised to the power 5, which is 0.07776, so subtracting from 1 gives 0.92224.
- A0.07776
- B0.92224Correct
- C0.7776
- D0.20000
Explanation
Use the complement: P(X≥1) = 1 − P(X=0) = 1 − (0.6)^5 = 1 − 0.07776 = 0.92224. The value 0.07776 is P(X=0) itself, which is the probability of no defective items, and 0.7776 is (0.6)^5 miscomputed as a power of 0.6 with four factors scaled wrongly.
Did you get it right without looking?
One question tells you little. A timed set on Theoretical Distributions shows your real accuracy, how long you take and where you lose marks.
More Theoretical Distributions questions
- A call centre in Pune receives faults reports at an average of 3 per hour, and the number of reports in an hour follows a Poisson distributi…
- A continuous random variable X follows a normal distribution with mean 50 and standard deviation 10. If Z represents the standardised normal…
- A quality control process inspects batches of electronic components. The inspection follows a binomial distribution where each component has…
- A pharmaceutical company observes that medication prescriptions follow a binomial distribution where the probability of a patient showing im…
- A factory produces ball bearings with a mean diameter of 8 mm and standard deviation of 0.2 mm, normally distributed. If the specification a…
- The weights of packets filled by a machine in Surat follow a normal distribution with standard deviation 15 grams. Using the relationship be…