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Three digits are chosen at random from 1,2,3,4,5,6,7,8 and 9 without repeating any digit. What is the probability that the product is odd?
- a)2/3
- b)7/48
- c)5/42
- d)5/108
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Three digits are chosen at random from 1,2,3,4,5,6,7,8 and 9 without r...
Total no. of 3-digit numbers = 9 x 8 x 7 = 504
For product to be odd, we have to choose only from odd numbers.
Total no. of 3-digit no. whose product are odd = 5 x 4 x 3 = 60
Required probability = 60/504 = 5/42
For product to be odd, we have to choose only from odd numbers.
Total no. of 3-digit no. whose product are odd = 5 x 4 x 3 = 60
Required probability = 60/504 = 5/42
Most Upvoted Answer
Three digits are chosen at random from 1,2,3,4,5,6,7,8 and 9 without r...
To find the probability that the product of three randomly chosen digits is odd, we need to consider two cases:
1. When the product of the three digits is odd
2. When the product of the three digits is even
Case 1: Product is Odd
In order for the product to be odd, at least one of the three digits must be odd. There are 5 odd digits in the given set: 1, 3, 5, 7, and 9.
To calculate the probability, we need to consider the number of favorable outcomes (where the product is odd) and the total number of possible outcomes.
Number of favorable outcomes:
We have 5 choices for the first digit, 8 choices for the second digit (since one digit has already been chosen and we cannot repeat), and 7 choices for the third digit. Therefore, the number of favorable outcomes is 5 * 8 * 7 = 280.
Total number of possible outcomes:
We have 9 choices for the first digit, 8 choices for the second digit (since one digit has already been chosen and we cannot repeat), and 7 choices for the third digit. Therefore, the total number of possible outcomes is 9 * 8 * 7 = 504.
Probability of the product being odd:
The probability is given by the number of favorable outcomes divided by the total number of possible outcomes:
P(Odd) = 280 / 504 = 5 / 9
Case 2: Product is Even
In order for the product to be even, all three digits must be even. There are 4 even digits in the given set: 2, 4, 6, and 8.
Number of favorable outcomes:
We have 4 choices for the first digit, 3 choices for the second digit (since one even digit has already been chosen and we cannot repeat), and 2 choices for the third digit. Therefore, the number of favorable outcomes is 4 * 3 * 2 = 24.
Total number of possible outcomes:
We have 9 choices for the first digit, 8 choices for the second digit (since one digit has already been chosen and we cannot repeat), and 7 choices for the third digit. Therefore, the total number of possible outcomes is 9 * 8 * 7 = 504.
Probability of the product being even:
The probability is given by the number of favorable outcomes divided by the total number of possible outcomes:
P(Even) = 24 / 504 = 1 / 21
Overall Probability:
The probability of the product being odd is equal to 1 minus the probability of the product being even:
P(Odd) = 1 - P(Even) = 1 - 1/21 = 20/21
Therefore, the probability that the product of three randomly chosen digits is odd is 5/9 or approximately 0.5556.
1. When the product of the three digits is odd
2. When the product of the three digits is even
Case 1: Product is Odd
In order for the product to be odd, at least one of the three digits must be odd. There are 5 odd digits in the given set: 1, 3, 5, 7, and 9.
To calculate the probability, we need to consider the number of favorable outcomes (where the product is odd) and the total number of possible outcomes.
Number of favorable outcomes:
We have 5 choices for the first digit, 8 choices for the second digit (since one digit has already been chosen and we cannot repeat), and 7 choices for the third digit. Therefore, the number of favorable outcomes is 5 * 8 * 7 = 280.
Total number of possible outcomes:
We have 9 choices for the first digit, 8 choices for the second digit (since one digit has already been chosen and we cannot repeat), and 7 choices for the third digit. Therefore, the total number of possible outcomes is 9 * 8 * 7 = 504.
Probability of the product being odd:
The probability is given by the number of favorable outcomes divided by the total number of possible outcomes:
P(Odd) = 280 / 504 = 5 / 9
Case 2: Product is Even
In order for the product to be even, all three digits must be even. There are 4 even digits in the given set: 2, 4, 6, and 8.
Number of favorable outcomes:
We have 4 choices for the first digit, 3 choices for the second digit (since one even digit has already been chosen and we cannot repeat), and 2 choices for the third digit. Therefore, the number of favorable outcomes is 4 * 3 * 2 = 24.
Total number of possible outcomes:
We have 9 choices for the first digit, 8 choices for the second digit (since one digit has already been chosen and we cannot repeat), and 7 choices for the third digit. Therefore, the total number of possible outcomes is 9 * 8 * 7 = 504.
Probability of the product being even:
The probability is given by the number of favorable outcomes divided by the total number of possible outcomes:
P(Even) = 24 / 504 = 1 / 21
Overall Probability:
The probability of the product being odd is equal to 1 minus the probability of the product being even:
P(Odd) = 1 - P(Even) = 1 - 1/21 = 20/21
Therefore, the probability that the product of three randomly chosen digits is odd is 5/9 or approximately 0.5556.
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Three digits are chosen at random from 1,2,3,4,5,6,7,8 and 9 without repeating any digit. What is the probability that the product is odd?a)2/3b)7/48c)5/42d)5/108Correct answer is option 'C'. Can you explain this answer?
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Three digits are chosen at random from 1,2,3,4,5,6,7,8 and 9 without repeating any digit. What is the probability that the product is odd?a)2/3b)7/48c)5/42d)5/108Correct answer is option 'C'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about Three digits are chosen at random from 1,2,3,4,5,6,7,8 and 9 without repeating any digit. What is the probability that the product is odd?a)2/3b)7/48c)5/42d)5/108Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three digits are chosen at random from 1,2,3,4,5,6,7,8 and 9 without repeating any digit. What is the probability that the product is odd?a)2/3b)7/48c)5/42d)5/108Correct answer is option 'C'. Can you explain this answer?.
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