English
Hindi
Telugu
Marathi

Question

Download Solution PDF

The chances of a defective screw in three boxes A, B, C are  and  respectively. A box is selected at random and a screw drawn from it at random is found to be defective. Find the probability that it came from box A.

Answer (Detailed Solution Below)

Option 3 :
Free Tests
View all Free tests >
Free
NDA 01/2025: English Subject Test
30 Qs. 120 Marks 30 Mins
Start Now

Detailed Solution

Download Solution PDF

Let E1, E2 and E3 denote the events of selecting box A, B, C respectively and A be the event that a screw selected at random is defective.

Then,

P(E1) = P(E2) = P(E3) = 1/3,

Then, by Baye’s theorem, required probability

= P(E1/A)

Download Solution PDF
Latest NDA Updates

Last updated on Jun 18, 2025

->UPSC has extended the UPSC NDA 2 Registration Date till 20th June 2025.

-> A total of 406 vacancies have been announced for NDA 2 Exam 2025.

->The NDA exam date 2025 has been announced. The written examination will be held on 14th September 2025.

-> The selection process for the NDA exam includes a Written Exam and SSB Interview.

-> Candidates who get successful selection under UPSC NDA will get a salary range between Rs. 15,600 to Rs. 39,100. 

-> Candidates must go through the NDA previous year question paper. Attempting the NDA mock test is also essential. 

Exams Tests Super Practice

More Baye's Theorem Questions

Q1.Three urns A, B and C contain 7 red, 5 black; 5 red, 7 black and 6 red, 6 black balls, respectively. One of the urn is selected at random and a ball is drawn from it. If the ball drawn is black, then the probability that it is drawn from urn A is :
Q2.A and B are two students. Their chances of solving a problem correctly are \(\frac{1}{3}\) and \(\frac{1}{4}\), respectively. If the probability of their making a common error is, \(\frac{1}{20}\) and they obtain the same answer, then the probability of their answer to be correct is
Q3.The chances of defective nuts in two boxes A and B are \(\rm \frac 1 5, \frac 1 7\) respectively. A box is selected at random and a nut drawn from it at random is found to be defective. The probability that it came from the box 'B' is
Q4.Prabhu is known to speak truth 3 out of 4 times. he throws a die and reports that it is a six. Find the probability that it is actually a six?
Q5.In the last week due to coronavirus outbreak, 200 children were tested positive, 400 adults were tested positive and 600 senior citizens were tested positive.The probability of them dying are 0.01, 0.03 and 0.15 respectively. If one of the person tested positive dies due to coronavirus what is the probability that he/she was a senior citizen.
Q6.A man is known to speak truth 2 out of 3 times. He throws a die and reports that number obtained is a four. Find the probability that the number obtained is actually a four.
Q7.One bag contain 3 white and 2 black balls, another bag contains 5 white and 3 black balls. If a bag is chosen at random and a ball is drawn from it, what is the chance that it is white?
Q8.Bag I contains 5 red and 7 green balls while another Bag II contains 6 red and 8 green balls. One ball is drawn at random from one of the bags and it is found to be red. Find the probability that it was drawn from Bag I.
Q9.In a bolt factory, machines X, Y, Z manufacture bolts that are respectively 25% 35%, and 40% of the factory’s total output. The machines X, Y, Z respectively produce 2%, 4% and 5% defective bolts. A bolt is drawn at random from the product and is found to be defective. What is the probability that it was manufactured by machine X? 
Q10.An insurance company insured 2000 scooter drivers, 4000 car drivers and 6000 truck drivers. The probabilities of an accident involving a scooter driver car driver and a truck driver are 0.01, 0.03 and 0.15 respectively. One of the insured persons meets with an accident. The probability that the person is a scooter driver is

More Probability Questions

Q1.Three perfect dice D1, D2 and D3 and are rolled. Let x, represent the numbers on D1, D2 and D3 respectively. What is the number of possible outcomes such that x < y < z?
Q2.Three perfect dice are rolled. Under the condition that no two show the same face, what is the probability that one of the faces shown is an ace (one)?
Q3.The occurrence of a disease in an industry is such that the workers have 20% chance of suffering from it. What is the probability that out of 6 workers chosen at random, 4 or more will suffer from the disease?
Q4.Two perfect dice are thrown. What C is the probability that the sum of the numbers on the faces is neither 9 nor 10?
Q5.Urn A contains 2 white and 2 black balls while urn B contains 3 white and 2 black balls. One ball is transferred from urn A to urn B and then a ball is drawn out of urn B. What is the probability that the ball is white?
Q6.A fair coin is tossed till two heads occur in succession. What is the probability that the number of tosses required is less than 6?  
Q7.A natural number x is chosen at random from the first 100 natural numbers. What is the probability that x2 + x > 50?
Q8.The letters of the word ZOOLOGY are arranged in all possible ways. What is the probability that the consonants and vowels occur alternatively?
Q9.A can hit a target 5 times in 6 shots, B can hit 4 times in 5 shots and C can hit 3 times in 4 shots. What is the probability that A and C may hit but B may lose?
Q10.A box contains 2 black, 4 yellow and 6 white balls. Three balls are drawn in succession with replacement. What is the probability that all three are of the same colour?
Suggested Test Series
View All >
Current Affairs (CA) 2025 Mega Pack for SSC/Railways/State Exam Mock Test
431 Total Tests with 4 Free Tests
Start Free Test
General Knowledge for All Defence Exams
317 Total Tests with   4 Free Tests
Start Free Test

NDA Important Links

ResultAdmit CardApplication FormEligibilitySalarySyllabus

More Mathematics Questions

Q1.If cosec θ + cot θ = p, then \(\rm\frac{p^2-1}{p^2+1}\) equal:
Q2.In a binomial distribution, if the mean is 6 and the standard deviation is √2, then what are the values of the parameters n and p respectively?
Q3.Three perfect dice D1, D2 and D3 and are rolled. Let x, represent the numbers on D1, D2 and D3 respectively. What is the number of possible outcomes such that x < y < z?
Q4.Three perfect dice are rolled. Under the condition that no two show the same face, what is the probability that one of the faces shown is an ace (one)?
Q5.The occurrence of a disease in an industry is such that the workers have 20% chance of suffering from it. What is the probability that out of 6 workers chosen at random, 4 or more will suffer from the disease?
Q6.Two perfect dice are thrown. What C is the probability that the sum of the numbers on the faces is neither 9 nor 10?
Q7.Urn A contains 2 white and 2 black balls while urn B contains 3 white and 2 black balls. One ball is transferred from urn A to urn B and then a ball is drawn out of urn B. What is the probability that the ball is white?
Q8.A fair coin is tossed till two heads occur in succession. What is the probability that the number of tosses required is less than 6?  
Q9.The mean of the series x1, x2...xn is x̅ If xn is replaced by k, then what is the new mean?
Q10.Let \(\rm \Sigma_{i=1}^9x_i^2=885\) If M is the mean and σ is the standard deviation of  x1, x2, x3.....x9 then what is the value of M2 + σ2?
Testbook Edu Solutions Pvt. Ltd.
1st & 2nd Floor, Zion Building,
Plot No. 273, Sector 10, Kharghar,
Navi Mumbai - 410210
support@testbook.com
Toll Free:1800 833 0800
Office Hours: 10 AM to 7 PM (all 7 days)
Company
About usCareers We are hiringTeach Online on TestbookPartnersMediaSitemap
Products
Test SeriesTestbook PassOnline CoursesOnline VideosPracticeBlogRefer & EarnBooks
Copyright © 2014-2022 Testbook Edu Solutions Pvt. Ltd.: All rights reserved
User PolicyTermsPrivacy
Hot Links： teen patti master official teen patti bodhi teen patti win teen patti master real cash teen patti flush