CA Foundation · Quantitative Aptitude · Probability
Three independent auditors, Mehta, Iyer and Khan, detect a particular error with probabilities 1/2, 1/3 and 1/4 respectively. What is the probability that the error is detected by exactly one of them?
The probability is 11/24. Add the three cases where exactly one auditor succeeds: 6/24 for Mehta, 3/24 for Iyer and 2/24 for Khan. Each case multiplies the success probability of one with the failure probabilities of the other two, since they are independent.
- A11/24Correct
- B1/4
- C1/24
- D3/4
Explanation
Only Mehta: 1/2 × 2/3 × 3/4 = 6/24. Only Iyer: 1/2 × 1/3 × 3/4 = 3/24. Only Khan: 1/2 × 2/3 × 1/4 = 2/24. Sum = 11/24. Check: none detect = 6/24 = 1/4 and 3/4 is at least one, which is a different quantity, so 3/4 is wrong.
Did you get it right without looking?
One question tells you little. A timed set on Probability shows your real accuracy, how long you take and where you lose marks.
More Probability questions
- Two fair dice are rolled together. What is the probability that the sum of the numbers shown is greater than 10?
- A box contains 4 defective and 6 good bulbs. Two bulbs are drawn one after another without replacement. Given that the second bulb is good, …
- A number is chosen at random from the integers 1 to 60. What is the probability that it is divisible by 4 or by 6 but not by both?
- A box contains 6 white and 4 black balls. Two balls are drawn one after another without replacement. What is the probability that the first …
- A committee of 3 members is to be chosen at random from 4 men and 3 women working in a Chennai firm. What is the probability that the commit…
- In a Mumbai firm, 70% of employees are graduates. Of the graduates, 40% are in the finance team, and of the non-graduates, 10% are in the fi…