GRE Exam > GRE Questions > Of the 20 lightbulbs in a box, 2 are defecti...
Start Learning for Free
Of the 20 lightbulbs in a box, 2 are defective. An inspector will select 2 lightbulbs simultaneously and at random from the box. What is the probability that neither of the lightbulbs selected will be defective?
Give your answer as a fraction.
[Numeric Ability Question]
Correct answer is '153/190'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
Of the 20 lightbulbs in a box, 2 are defective. An inspector will sel...
To find the probability that neither of the lightbulbs selected will be defective, we can use the concept of combinations.
Let's break down the problem with the given information:
Total number of lightbulbs in the box = 20
Number of defective lightbulbs = 2
We need to select 2 lightbulbs simultaneously and at random from the box.
Step 1: Finding the total number of ways to select 2 lightbulbs from the box
To find this, we can use the concept of combinations. The formula for combinations is given by:
nCr = n! / (r! * (n-r)!)
where n is the total number of items, r is the number of items to be selected, and ! denotes factorial.
In our case, we need to find the number of ways to select 2 lightbulbs from a total of 20, so n = 20 and r = 2.
20C2 = 20! / (2! * (20-2)!)
= 20! / (2! * 18!)
= (20 * 19 * 18!) / (2! * 18!)
= (20 * 19) / 2
= 380
So, there are 380 different ways to select 2 lightbulbs from the box.
Step 2: Finding the number of ways to select 2 non-defective lightbulbs
Since there are 2 defective lightbulbs, the remaining 18 lightbulbs in the box are non-defective. So, we need to select 2 lightbulbs from these 18 non-defective lightbulbs.
18C2 = 18! / (2! * (18-2)!)
= 18! / (2! * 16!)
= (18 * 17) / 2
= 153
There are 153 different ways to select 2 non-defective lightbulbs.
Step 3: Calculating the probability
The probability is given by the number of favorable outcomes divided by the total number of outcomes.
Number of favorable outcomes = number of ways to select 2 non-defective lightbulbs = 153
Total number of outcomes = number of ways to select 2 lightbulbs from the box = 380
Probability = Number of favorable outcomes / Total number of outcomes
= 153 / 380
= 153/190
Therefore, the probability that neither of the lightbulbs selected will be defective is 153/190.
Let's break down the problem with the given information:
Total number of lightbulbs in the box = 20
Number of defective lightbulbs = 2
We need to select 2 lightbulbs simultaneously and at random from the box.
Step 1: Finding the total number of ways to select 2 lightbulbs from the box
To find this, we can use the concept of combinations. The formula for combinations is given by:
nCr = n! / (r! * (n-r)!)
where n is the total number of items, r is the number of items to be selected, and ! denotes factorial.
In our case, we need to find the number of ways to select 2 lightbulbs from a total of 20, so n = 20 and r = 2.
20C2 = 20! / (2! * (20-2)!)
= 20! / (2! * 18!)
= (20 * 19 * 18!) / (2! * 18!)
= (20 * 19) / 2
= 380
So, there are 380 different ways to select 2 lightbulbs from the box.
Step 2: Finding the number of ways to select 2 non-defective lightbulbs
Since there are 2 defective lightbulbs, the remaining 18 lightbulbs in the box are non-defective. So, we need to select 2 lightbulbs from these 18 non-defective lightbulbs.
18C2 = 18! / (2! * (18-2)!)
= 18! / (2! * 16!)
= (18 * 17) / 2
= 153
There are 153 different ways to select 2 non-defective lightbulbs.
Step 3: Calculating the probability
The probability is given by the number of favorable outcomes divided by the total number of outcomes.
Number of favorable outcomes = number of ways to select 2 non-defective lightbulbs = 153
Total number of outcomes = number of ways to select 2 lightbulbs from the box = 380
Probability = Number of favorable outcomes / Total number of outcomes
= 153 / 380
= 153/190
Therefore, the probability that neither of the lightbulbs selected will be defective is 153/190.
Free Test
FREE
| Start Free Test |
Community Answer
Of the 20 lightbulbs in a box, 2 are defective. An inspector will sel...
The desired probability corresponds to the fraction the number of ways that 2 lightbulbs, both of which are not defective, can be chosen / the number of ways that 2 lightbulbs can be chosen
In order to calculate the desired probability, you need to calculate the values of the numerator and the denominator of this fraction.
Approach is to look at the selection of the two lightbulbs separately. The problem states that lightbulbs are selected simultaneously. However, the timing of the selection only ensures that the same lightbulb is not chosen twice. This is equivalent to choosing one lightbulb first and then choosing a second lightbulb without replacing the first. The probability that the first lightbulb selected will not be defective is 18/20. If the first lightbulb selected is not defective, there will be 19 lightbulbs left to choose from, 17 of which are not defective. Thus, the probability that the second lightbulb selected will not be defective is 17/19. The probability that both lightbulbs selected will not be defective is the product of these two probabilities. Thus, the desired probability is (18/20)(17/19) = 153/119. The correct answer is 153/119.
Attention GRE Students!
To make sure you are not studying endlessly, EduRev has designed GRE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in GRE.
|
Explore Courses for GRE exam
|
|
Similar GRE Doubts
Top Courses for GREView all
Of the 20 lightbulbs in a box, 2 are defective. An inspector will select 2 lightbulbs simultaneously and at random from the box. What is the probability that neither of the lightbulbs selected will be defective?Give your answer as a fraction.[Numeric Ability Question]Correct answer is '153/190'. Can you explain this answer?
Question Description
Of the 20 lightbulbs in a box, 2 are defective. An inspector will select 2 lightbulbs simultaneously and at random from the box. What is the probability that neither of the lightbulbs selected will be defective?Give your answer as a fraction.[Numeric Ability Question]Correct answer is '153/190'. Can you explain this answer? for GRE 2024 is part of GRE preparation. The Question and answers have been prepared according to the GRE exam syllabus. Information about Of the 20 lightbulbs in a box, 2 are defective. An inspector will select 2 lightbulbs simultaneously and at random from the box. What is the probability that neither of the lightbulbs selected will be defective?Give your answer as a fraction.[Numeric Ability Question]Correct answer is '153/190'. Can you explain this answer? covers all topics & solutions for GRE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Of the 20 lightbulbs in a box, 2 are defective. An inspector will select 2 lightbulbs simultaneously and at random from the box. What is the probability that neither of the lightbulbs selected will be defective?Give your answer as a fraction.[Numeric Ability Question]Correct answer is '153/190'. Can you explain this answer?.
Of the 20 lightbulbs in a box, 2 are defective. An inspector will select 2 lightbulbs simultaneously and at random from the box. What is the probability that neither of the lightbulbs selected will be defective?Give your answer as a fraction.[Numeric Ability Question]Correct answer is '153/190'. Can you explain this answer? for GRE 2024 is part of GRE preparation. The Question and answers have been prepared according to the GRE exam syllabus. Information about Of the 20 lightbulbs in a box, 2 are defective. An inspector will select 2 lightbulbs simultaneously and at random from the box. What is the probability that neither of the lightbulbs selected will be defective?Give your answer as a fraction.[Numeric Ability Question]Correct answer is '153/190'. Can you explain this answer? covers all topics & solutions for GRE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Of the 20 lightbulbs in a box, 2 are defective. An inspector will select 2 lightbulbs simultaneously and at random from the box. What is the probability that neither of the lightbulbs selected will be defective?Give your answer as a fraction.[Numeric Ability Question]Correct answer is '153/190'. Can you explain this answer?.
Solutions for Of the 20 lightbulbs in a box, 2 are defective. An inspector will select 2 lightbulbs simultaneously and at random from the box. What is the probability that neither of the lightbulbs selected will be defective?Give your answer as a fraction.[Numeric Ability Question]Correct answer is '153/190'. Can you explain this answer? in English & in Hindi are available as part of our courses for GRE.
Download more important topics, notes, lectures and mock test series for GRE Exam by signing up for free.
Here you can find the meaning of Of the 20 lightbulbs in a box, 2 are defective. An inspector will select 2 lightbulbs simultaneously and at random from the box. What is the probability that neither of the lightbulbs selected will be defective?Give your answer as a fraction.[Numeric Ability Question]Correct answer is '153/190'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Of the 20 lightbulbs in a box, 2 are defective. An inspector will select 2 lightbulbs simultaneously and at random from the box. What is the probability that neither of the lightbulbs selected will be defective?Give your answer as a fraction.[Numeric Ability Question]Correct answer is '153/190'. Can you explain this answer?, a detailed solution for Of the 20 lightbulbs in a box, 2 are defective. An inspector will select 2 lightbulbs simultaneously and at random from the box. What is the probability that neither of the lightbulbs selected will be defective?Give your answer as a fraction.[Numeric Ability Question]Correct answer is '153/190'. Can you explain this answer? has been provided alongside types of Of the 20 lightbulbs in a box, 2 are defective. An inspector will select 2 lightbulbs simultaneously and at random from the box. What is the probability that neither of the lightbulbs selected will be defective?Give your answer as a fraction.[Numeric Ability Question]Correct answer is '153/190'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Of the 20 lightbulbs in a box, 2 are defective. An inspector will select 2 lightbulbs simultaneously and at random from the box. What is the probability that neither of the lightbulbs selected will be defective?Give your answer as a fraction.[Numeric Ability Question]Correct answer is '153/190'. Can you explain this answer? tests, examples and also practice GRE tests.
|
|
Explore Courses for GRE 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