CAT Exam > CAT Questions > Three screws are drawn at random from a lot ...
Start Learning for Free
Three screws are drawn at random from a lot of 100 screws, 10 of which are defective. The probability of the event that all 3 screws drawn are non-defective, assuming that the screws are drawn without replacement, is
- a)70.65%
- b)71.65%
- c)74.65%
- d)72.65%
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
Three screws are drawn at random from a lot of 100 screws, 10 of whic...
The probability of the event that all 3 screws drawn are non-defective =
(90/100) x (89/99) x (88/98) = 72.65%
Free Test
FREE
| Start Free Test |
Community Answer
Three screws are drawn at random from a lot of 100 screws, 10 of whic...
To find the probability that all 3 screws drawn are non-defective, we need to find the ratio of the number of favorable outcomes (i.e., when all 3 screws are non-defective) to the total number of possible outcomes.
Total number of screws = 100
Number of defective screws = 10
Step 1: Finding the probability of selecting the first non-defective screw
When the first screw is drawn, there are 100 screws in total, out of which 10 are defective. Therefore, the probability of selecting a non-defective screw at the first draw is:
P(First non-defective screw) = (100 - 10) / 100 = 90 / 100 = 9 / 10
Step 2: Finding the probability of selecting the second non-defective screw
After the first non-defective screw is drawn, there are 99 screws left, out of which 9 are non-defective. Therefore, the probability of selecting a non-defective screw at the second draw is:
P(Second non-defective screw) = (99 - 9) / 99 = 90 / 99
Step 3: Finding the probability of selecting the third non-defective screw
After the second non-defective screw is drawn, there are 98 screws left, out of which 8 are non-defective. Therefore, the probability of selecting a non-defective screw at the third draw is:
P(Third non-defective screw) = (98 - 8) / 98 = 90 / 98 = 45 / 49
Step 4: Finding the probability of all 3 screws being non-defective
Since the screws are drawn without replacement, the probabilities calculated in steps 1, 2, and 3 are multiplied together to find the probability of all 3 screws being non-defective:
P(All 3 screws non-defective) = P(First non-defective screw) * P(Second non-defective screw) * P(Third non-defective screw)
= (9/10) * (90/99) * (45/49)
= 0.9 * 0.9091 * 0.9184
≈ 0.7465
Therefore, the probability of all 3 screws drawn being non-defective is approximately 74.65%, which corresponds to option (d).
Total number of screws = 100
Number of defective screws = 10
Step 1: Finding the probability of selecting the first non-defective screw
When the first screw is drawn, there are 100 screws in total, out of which 10 are defective. Therefore, the probability of selecting a non-defective screw at the first draw is:
P(First non-defective screw) = (100 - 10) / 100 = 90 / 100 = 9 / 10
Step 2: Finding the probability of selecting the second non-defective screw
After the first non-defective screw is drawn, there are 99 screws left, out of which 9 are non-defective. Therefore, the probability of selecting a non-defective screw at the second draw is:
P(Second non-defective screw) = (99 - 9) / 99 = 90 / 99
Step 3: Finding the probability of selecting the third non-defective screw
After the second non-defective screw is drawn, there are 98 screws left, out of which 8 are non-defective. Therefore, the probability of selecting a non-defective screw at the third draw is:
P(Third non-defective screw) = (98 - 8) / 98 = 90 / 98 = 45 / 49
Step 4: Finding the probability of all 3 screws being non-defective
Since the screws are drawn without replacement, the probabilities calculated in steps 1, 2, and 3 are multiplied together to find the probability of all 3 screws being non-defective:
P(All 3 screws non-defective) = P(First non-defective screw) * P(Second non-defective screw) * P(Third non-defective screw)
= (9/10) * (90/99) * (45/49)
= 0.9 * 0.9091 * 0.9184
≈ 0.7465
Therefore, the probability of all 3 screws drawn being non-defective is approximately 74.65%, which corresponds to option (d).
Attention CAT Students!
To make sure you are not studying endlessly, EduRev has designed CAT study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CAT.
|
Explore Courses for CAT exam
|
|
Similar CAT Doubts
Top Courses for CATView all
Three screws are drawn at random from a lot of 100 screws, 10 of which are defective. The probability of the event that all 3 screws drawn are non-defective, assuming that the screws are drawn without replacement, isa)70.65%b)71.65%c)74.65%d)72.65%Correct answer is option 'D'. Can you explain this answer?
Question Description
Three screws are drawn at random from a lot of 100 screws, 10 of which are defective. The probability of the event that all 3 screws drawn are non-defective, assuming that the screws are drawn without replacement, isa)70.65%b)71.65%c)74.65%d)72.65%Correct answer is option 'D'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Three screws are drawn at random from a lot of 100 screws, 10 of which are defective. The probability of the event that all 3 screws drawn are non-defective, assuming that the screws are drawn without replacement, isa)70.65%b)71.65%c)74.65%d)72.65%Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three screws are drawn at random from a lot of 100 screws, 10 of which are defective. The probability of the event that all 3 screws drawn are non-defective, assuming that the screws are drawn without replacement, isa)70.65%b)71.65%c)74.65%d)72.65%Correct answer is option 'D'. Can you explain this answer?.
Three screws are drawn at random from a lot of 100 screws, 10 of which are defective. The probability of the event that all 3 screws drawn are non-defective, assuming that the screws are drawn without replacement, isa)70.65%b)71.65%c)74.65%d)72.65%Correct answer is option 'D'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Three screws are drawn at random from a lot of 100 screws, 10 of which are defective. The probability of the event that all 3 screws drawn are non-defective, assuming that the screws are drawn without replacement, isa)70.65%b)71.65%c)74.65%d)72.65%Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three screws are drawn at random from a lot of 100 screws, 10 of which are defective. The probability of the event that all 3 screws drawn are non-defective, assuming that the screws are drawn without replacement, isa)70.65%b)71.65%c)74.65%d)72.65%Correct answer is option 'D'. Can you explain this answer?.
Solutions for Three screws are drawn at random from a lot of 100 screws, 10 of which are defective. The probability of the event that all 3 screws drawn are non-defective, assuming that the screws are drawn without replacement, isa)70.65%b)71.65%c)74.65%d)72.65%Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
Here you can find the meaning of Three screws are drawn at random from a lot of 100 screws, 10 of which are defective. The probability of the event that all 3 screws drawn are non-defective, assuming that the screws are drawn without replacement, isa)70.65%b)71.65%c)74.65%d)72.65%Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Three screws are drawn at random from a lot of 100 screws, 10 of which are defective. The probability of the event that all 3 screws drawn are non-defective, assuming that the screws are drawn without replacement, isa)70.65%b)71.65%c)74.65%d)72.65%Correct answer is option 'D'. Can you explain this answer?, a detailed solution for Three screws are drawn at random from a lot of 100 screws, 10 of which are defective. The probability of the event that all 3 screws drawn are non-defective, assuming that the screws are drawn without replacement, isa)70.65%b)71.65%c)74.65%d)72.65%Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of Three screws are drawn at random from a lot of 100 screws, 10 of which are defective. The probability of the event that all 3 screws drawn are non-defective, assuming that the screws are drawn without replacement, isa)70.65%b)71.65%c)74.65%d)72.65%Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Three screws are drawn at random from a lot of 100 screws, 10 of which are defective. The probability of the event that all 3 screws drawn are non-defective, assuming that the screws are drawn without replacement, isa)70.65%b)71.65%c)74.65%d)72.65%Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice CAT tests.
|
|
Explore Courses for CAT exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup