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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.
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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?
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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?.
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