UPSC Exam > UPSC Questions > Four digits 1,2,4 and 6 are selected at rando...
Start Learning for Free
Four digits 1,2,4 and 6 are selected at random to form a four digit number. What is the probability that the number so formed, would be divisible by 4 ?
(a) 1/2
(b) 1/5
(c) 1/4
(d) 1/3?
(a) 1/2
(b) 1/5
(c) 1/4
(d) 1/3?
Most Upvoted Answer
Four digits 1,2,4 and 6 are selected at random to form a four digit nu...
Probability of forming a four digit number divisible by 4
- To determine the probability of forming a four-digit number that is divisible by 4 using the digits 1, 2, 4, and 6, we need to consider the total number of possible outcomes and the number of favorable outcomes.
Total number of outcomes
- There are a total of 4 digits to choose from to form a four-digit number. So, the total number of ways to select the first digit is 4, the second digit is 3, the third digit is 2, and the fourth digit is 1. Therefore, the total number of possible outcomes is 4 x 3 x 2 x 1 = 24.
Favorable outcomes
- A number is divisible by 4 if the last two digits form a number that is divisible by 4. Out of the given digits 1, 2, 4, and 6, only the pairs 12 and 24 are divisible by 4. So, for the last two digits, there are 2 ways to choose them.
- For the first two digits, we have 2 choices left for the first digit (1 or 2) and 2 choices for the second digit (the remaining one out of 1 and 2). Therefore, there are 2 x 2 = 4 ways to choose the first two digits.
- Hence, the total number of favorable outcomes is 2 x 4 = 8.
Calculating the probability
- Probability = Number of favorable outcomes / Total number of outcomes
- Probability = 8 / 24 = 1/3
Therefore, the probability that the four-digit number formed using the digits 1, 2, 4, and 6 would be divisible by 4 is 1/3. So, the correct answer is (d) 1/3.
- To determine the probability of forming a four-digit number that is divisible by 4 using the digits 1, 2, 4, and 6, we need to consider the total number of possible outcomes and the number of favorable outcomes.
Total number of outcomes
- There are a total of 4 digits to choose from to form a four-digit number. So, the total number of ways to select the first digit is 4, the second digit is 3, the third digit is 2, and the fourth digit is 1. Therefore, the total number of possible outcomes is 4 x 3 x 2 x 1 = 24.
Favorable outcomes
- A number is divisible by 4 if the last two digits form a number that is divisible by 4. Out of the given digits 1, 2, 4, and 6, only the pairs 12 and 24 are divisible by 4. So, for the last two digits, there are 2 ways to choose them.
- For the first two digits, we have 2 choices left for the first digit (1 or 2) and 2 choices for the second digit (the remaining one out of 1 and 2). Therefore, there are 2 x 2 = 4 ways to choose the first two digits.
- Hence, the total number of favorable outcomes is 2 x 4 = 8.
Calculating the probability
- Probability = Number of favorable outcomes / Total number of outcomes
- Probability = 8 / 24 = 1/3
Therefore, the probability that the four-digit number formed using the digits 1, 2, 4, and 6 would be divisible by 4 is 1/3. So, the correct answer is (d) 1/3.
Attention UPSC Students!
To make sure you are not studying endlessly, EduRev has designed UPSC study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in UPSC.
|
Explore Courses for UPSC exam
|
|
Similar UPSC Doubts
Top Courses for UPSCView all
Four digits 1,2,4 and 6 are selected at random to form a four digit number. What is the probability that the number so formed, would be divisible by 4 ? (a) 1/2 (b) 1/5 (c) 1/4 (d) 1/3?
Question Description
Four digits 1,2,4 and 6 are selected at random to form a four digit number. What is the probability that the number so formed, would be divisible by 4 ? (a) 1/2 (b) 1/5 (c) 1/4 (d) 1/3? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Four digits 1,2,4 and 6 are selected at random to form a four digit number. What is the probability that the number so formed, would be divisible by 4 ? (a) 1/2 (b) 1/5 (c) 1/4 (d) 1/3? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Four digits 1,2,4 and 6 are selected at random to form a four digit number. What is the probability that the number so formed, would be divisible by 4 ? (a) 1/2 (b) 1/5 (c) 1/4 (d) 1/3?.
Four digits 1,2,4 and 6 are selected at random to form a four digit number. What is the probability that the number so formed, would be divisible by 4 ? (a) 1/2 (b) 1/5 (c) 1/4 (d) 1/3? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Four digits 1,2,4 and 6 are selected at random to form a four digit number. What is the probability that the number so formed, would be divisible by 4 ? (a) 1/2 (b) 1/5 (c) 1/4 (d) 1/3? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Four digits 1,2,4 and 6 are selected at random to form a four digit number. What is the probability that the number so formed, would be divisible by 4 ? (a) 1/2 (b) 1/5 (c) 1/4 (d) 1/3?.
Solutions for Four digits 1,2,4 and 6 are selected at random to form a four digit number. What is the probability that the number so formed, would be divisible by 4 ? (a) 1/2 (b) 1/5 (c) 1/4 (d) 1/3? in English & in Hindi are available as part of our courses for UPSC.
Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of Four digits 1,2,4 and 6 are selected at random to form a four digit number. What is the probability that the number so formed, would be divisible by 4 ? (a) 1/2 (b) 1/5 (c) 1/4 (d) 1/3? defined & explained in the simplest way possible. Besides giving the explanation of
Four digits 1,2,4 and 6 are selected at random to form a four digit number. What is the probability that the number so formed, would be divisible by 4 ? (a) 1/2 (b) 1/5 (c) 1/4 (d) 1/3?, a detailed solution for Four digits 1,2,4 and 6 are selected at random to form a four digit number. What is the probability that the number so formed, would be divisible by 4 ? (a) 1/2 (b) 1/5 (c) 1/4 (d) 1/3? has been provided alongside types of Four digits 1,2,4 and 6 are selected at random to form a four digit number. What is the probability that the number so formed, would be divisible by 4 ? (a) 1/2 (b) 1/5 (c) 1/4 (d) 1/3? theory, EduRev gives you an
ample number of questions to practice Four digits 1,2,4 and 6 are selected at random to form a four digit number. What is the probability that the number so formed, would be divisible by 4 ? (a) 1/2 (b) 1/5 (c) 1/4 (d) 1/3? tests, examples and also practice UPSC tests.
|
|
Explore Courses for UPSC exam
|
|
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