GMAT Exam > GMAT Questions > The probability of a manufacturing company pr...
Start Learning for Free
The probability of a manufacturing company producing a defective item is 0.1. If 5 items are drawn at random from a set of 100 distinct items, what is the probability that at least 2 items would be defective?
- a)1-0.94 x 1.4
- b)1-0.94
- c)1-0.95
- d)1-0.94 x 0.5
- e)1-0.94 x 0.1
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
The probability of a manufacturing company producing a defective item ...
Given
- P(defective item) = 0.1
- P(non-defective item) = 0.9
- Total number of items = 100
- Number of items drawn = 5
To Find: Probability that at-least 2 items will be defective
Approach
- Event= getting (2, 3, 4, or 5) items defective
- Non-Event = getting (0 or 1) item defective
- So, we will opt for the non-event method
- P(Event) = 1 – P(non-event)
- Non- Event: Getting 0 or 1 item defective
- Case-I: Getting 0 defective items
- Total number of ways in which 0 selected items can be defective = Item-1 is non-defective AND item-2 is non-defective…………AND item-5 is non defective
- = P(item-1 being non-defective) * P(item-2 being non-defective) *P(item-3 being non-defective)……….* P(item-5 being non-defective)
- Case-II: Getting 1 defective item
- P(getting 1 item defective AND 4 items non-defective) = Number of ways of selecting 1 item from 5 items * P(an item being defective) * P(an item being non-defective) *…..P(item being non-defective)
- P(Non-Event) = P(case-I) + P(case-II)
Working Out
- Non-Event: getting 0 or 1 defective items
- Case-I: Getting 0 defective items
- P(getting 0 defective items) = P(item-1 being non-defective) *P(item-2 being non-defective) …….P(item-5 being non-defective) =0.95…….(1)
- Case-II: getting 1 defective item
- P(getting 1 item defective AND 4 items non-defective) = Number of ways of selecting 1 item from 5 items * P(an item being defective) * P(an item being non-defective) *…..P(item being non-defective)
- P(Non-event-) =
- 2. P(Event) = 1- P(non-Event) =
Most Upvoted Answer
The probability of a manufacturing company producing a defective item ...
To solve this problem, we can use the concept of binomial distribution. Let's break down the problem into smaller steps to find the probability of at least 2 defective items.
Step 1: Finding the probability of exactly 2 defective items
The probability of producing a defective item is given as 0.1. Therefore, the probability of producing a non-defective item is 1 - 0.1 = 0.9.
We can use the binomial probability formula to find the probability of exactly 2 defective items out of 5 drawn items:
P(X = 2) = (5C2) * (0.1^2) * (0.9^3)
= (5! / (2! * 3!)) * (0.1^2) * (0.9^3)
= (10) * (0.01) * (0.729)
= 0.0729
Step 2: Finding the probability of exactly 3 defective items
Using the same formula, we can find the probability of exactly 3 defective items out of 5 drawn items:
P(X = 3) = (5C3) * (0.1^3) * (0.9^2)
= (5! / (3! * 2!)) * (0.001) * (0.81)
= 0.0729
Step 3: Finding the probability of at least 2 defective items
To find the probability of at least 2 defective items, we need to find the sum of the probabilities of exactly 2, 3, 4, and 5 defective items.
P(at least 2) = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)
Since the number of defective items can only range from 0 to 5, we know that P(X = 4) and P(X = 5) will be very small probabilities, approaching zero. Therefore, we can ignore them in our calculation.
P(at least 2) ≈ P(X = 2) + P(X = 3)
P(at least 2) ≈ 0.0729 + 0.0729
P(at least 2) ≈ 0.1458
Step 4: Finding the final probability
The question asks for the probability that at least 2 items would be defective, but the answer choices are given in the form of 1 minus the probability. Therefore, we can calculate:
Final probability = 1 - P(at least 2)
Final probability = 1 - 0.1458
Final probability ≈ 0.8542
The closest answer choice to 0.8542 is option A, which is 1 - 0.94 × 1.4.
Step 1: Finding the probability of exactly 2 defective items
The probability of producing a defective item is given as 0.1. Therefore, the probability of producing a non-defective item is 1 - 0.1 = 0.9.
We can use the binomial probability formula to find the probability of exactly 2 defective items out of 5 drawn items:
P(X = 2) = (5C2) * (0.1^2) * (0.9^3)
= (5! / (2! * 3!)) * (0.1^2) * (0.9^3)
= (10) * (0.01) * (0.729)
= 0.0729
Step 2: Finding the probability of exactly 3 defective items
Using the same formula, we can find the probability of exactly 3 defective items out of 5 drawn items:
P(X = 3) = (5C3) * (0.1^3) * (0.9^2)
= (5! / (3! * 2!)) * (0.001) * (0.81)
= 0.0729
Step 3: Finding the probability of at least 2 defective items
To find the probability of at least 2 defective items, we need to find the sum of the probabilities of exactly 2, 3, 4, and 5 defective items.
P(at least 2) = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)
Since the number of defective items can only range from 0 to 5, we know that P(X = 4) and P(X = 5) will be very small probabilities, approaching zero. Therefore, we can ignore them in our calculation.
P(at least 2) ≈ P(X = 2) + P(X = 3)
P(at least 2) ≈ 0.0729 + 0.0729
P(at least 2) ≈ 0.1458
Step 4: Finding the final probability
The question asks for the probability that at least 2 items would be defective, but the answer choices are given in the form of 1 minus the probability. Therefore, we can calculate:
Final probability = 1 - P(at least 2)
Final probability = 1 - 0.1458
Final probability ≈ 0.8542
The closest answer choice to 0.8542 is option A, which is 1 - 0.94 × 1.4.
Attention GMAT Students!
To make sure you are not studying endlessly, EduRev has designed GMAT study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in GMAT.
|
Explore Courses for GMAT exam
|
|
Similar GMAT Doubts
Top Courses for GMATView all
The probability of a manufacturing company producing a defective item is 0.1. If 5 items are drawn at random from a set of 100 distinct items, what is the probability that at least 2 items would be defective?a)1-0.94x 1.4b)1-0.94c)1-0.95d)1-0.94x 0.5e)1-0.94 x 0.1Correct answer is option 'A'. Can you explain this answer?
Question Description
The probability of a manufacturing company producing a defective item is 0.1. If 5 items are drawn at random from a set of 100 distinct items, what is the probability that at least 2 items would be defective?a)1-0.94x 1.4b)1-0.94c)1-0.95d)1-0.94x 0.5e)1-0.94 x 0.1Correct answer is option 'A'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about The probability of a manufacturing company producing a defective item is 0.1. If 5 items are drawn at random from a set of 100 distinct items, what is the probability that at least 2 items would be defective?a)1-0.94x 1.4b)1-0.94c)1-0.95d)1-0.94x 0.5e)1-0.94 x 0.1Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The probability of a manufacturing company producing a defective item is 0.1. If 5 items are drawn at random from a set of 100 distinct items, what is the probability that at least 2 items would be defective?a)1-0.94x 1.4b)1-0.94c)1-0.95d)1-0.94x 0.5e)1-0.94 x 0.1Correct answer is option 'A'. Can you explain this answer?.
The probability of a manufacturing company producing a defective item is 0.1. If 5 items are drawn at random from a set of 100 distinct items, what is the probability that at least 2 items would be defective?a)1-0.94x 1.4b)1-0.94c)1-0.95d)1-0.94x 0.5e)1-0.94 x 0.1Correct answer is option 'A'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about The probability of a manufacturing company producing a defective item is 0.1. If 5 items are drawn at random from a set of 100 distinct items, what is the probability that at least 2 items would be defective?a)1-0.94x 1.4b)1-0.94c)1-0.95d)1-0.94x 0.5e)1-0.94 x 0.1Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The probability of a manufacturing company producing a defective item is 0.1. If 5 items are drawn at random from a set of 100 distinct items, what is the probability that at least 2 items would be defective?a)1-0.94x 1.4b)1-0.94c)1-0.95d)1-0.94x 0.5e)1-0.94 x 0.1Correct answer is option 'A'. Can you explain this answer?.
Solutions for The probability of a manufacturing company producing a defective item is 0.1. If 5 items are drawn at random from a set of 100 distinct items, what is the probability that at least 2 items would be defective?a)1-0.94x 1.4b)1-0.94c)1-0.95d)1-0.94x 0.5e)1-0.94 x 0.1Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
Download more important topics, notes, lectures and mock test series for GMAT Exam by signing up for free.
Here you can find the meaning of The probability of a manufacturing company producing a defective item is 0.1. If 5 items are drawn at random from a set of 100 distinct items, what is the probability that at least 2 items would be defective?a)1-0.94x 1.4b)1-0.94c)1-0.95d)1-0.94x 0.5e)1-0.94 x 0.1Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The probability of a manufacturing company producing a defective item is 0.1. If 5 items are drawn at random from a set of 100 distinct items, what is the probability that at least 2 items would be defective?a)1-0.94x 1.4b)1-0.94c)1-0.95d)1-0.94x 0.5e)1-0.94 x 0.1Correct answer is option 'A'. Can you explain this answer?, a detailed solution for The probability of a manufacturing company producing a defective item is 0.1. If 5 items are drawn at random from a set of 100 distinct items, what is the probability that at least 2 items would be defective?a)1-0.94x 1.4b)1-0.94c)1-0.95d)1-0.94x 0.5e)1-0.94 x 0.1Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of The probability of a manufacturing company producing a defective item is 0.1. If 5 items are drawn at random from a set of 100 distinct items, what is the probability that at least 2 items would be defective?a)1-0.94x 1.4b)1-0.94c)1-0.95d)1-0.94x 0.5e)1-0.94 x 0.1Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The probability of a manufacturing company producing a defective item is 0.1. If 5 items are drawn at random from a set of 100 distinct items, what is the probability that at least 2 items would be defective?a)1-0.94x 1.4b)1-0.94c)1-0.95d)1-0.94x 0.5e)1-0.94 x 0.1Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice GMAT tests.
|
|
Explore Courses for GMAT 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
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup