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Three dice are thrown together. What is the probability of getting sum of the numbers on the three dice to be even when it is known that number which appeared on the second die was odd?
- a)1/4
- b)1/2
- c)1/3
- d)2/3
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Three dice are thrown together. What is the probability of getting su...
It is told that the sum of the three numbers must be even and the number on the second dice is odd.
It means that the number which comes on the first and third dice must be even and odd in any order.
Case-1
First dice even, third dice odd.
So total number of ways = 3 X 3 = 9 ways
Case-2
First dice odd, third dice even.
So total number of ways = 3 X 3 = 9 ways
Hence total number of favorable ways = 9 + 9 = 18 ways
Total number of possible ways = 6 X 6 = 36 ways
Therefore required probability = (18/36) = 1/2
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Community Answer
Three dice are thrown together. What is the probability of getting su...
Problem Analysis
We need to find the probability of getting a sum of the numbers on the three dice to be even, given that the number on the second die is odd. Let's consider each die separately and analyze the possible outcomes.
Possible Outcomes for the First Die
- The first die can have any number from 1 to 6, so there are 6 possible outcomes.
Possible Outcomes for the Second Die
- The second die is odd, so it can have any number from 1 to 6, excluding the even numbers. Therefore, there are 3 possible outcomes.
Possible Outcomes for the Third Die
- The third die can have any number from 1 to 6, so there are 6 possible outcomes.
Total Possible Outcomes
The total number of possible outcomes is the product of the possible outcomes for each die, which is 6 * 3 * 6 = 108.
Favorable Outcomes
To calculate the number of favorable outcomes, we need to consider the cases where the sum of the three dice is even.
Case 1: First Die is Even
If the first die is even, there are 3 possible outcomes for the second die (odd numbers) and 6 possible outcomes for the third die (any number). Therefore, there are 3 * 6 = 18 favorable outcomes for this case.
Case 2: First Die is Odd
If the first die is odd, there are 3 possible outcomes for the second die (odd numbers) and 6 possible outcomes for the third die (any number). Therefore, there are 3 * 6 = 18 favorable outcomes for this case.
Total Favorable Outcomes
The total number of favorable outcomes is the sum of the favorable outcomes for each case, which is 18 + 18 = 36.
Probability
The probability of getting a sum of the numbers on the three dice to be even, given that the number on the second die is odd, is the ratio of the number of favorable outcomes to the total number of possible outcomes.
Probability = Favorable Outcomes / Total Possible Outcomes
Probability = 36 / 108
Probability = 1/3
Therefore, the correct answer is option C) 1/3.
We need to find the probability of getting a sum of the numbers on the three dice to be even, given that the number on the second die is odd. Let's consider each die separately and analyze the possible outcomes.
Possible Outcomes for the First Die
- The first die can have any number from 1 to 6, so there are 6 possible outcomes.
Possible Outcomes for the Second Die
- The second die is odd, so it can have any number from 1 to 6, excluding the even numbers. Therefore, there are 3 possible outcomes.
Possible Outcomes for the Third Die
- The third die can have any number from 1 to 6, so there are 6 possible outcomes.
Total Possible Outcomes
The total number of possible outcomes is the product of the possible outcomes for each die, which is 6 * 3 * 6 = 108.
Favorable Outcomes
To calculate the number of favorable outcomes, we need to consider the cases where the sum of the three dice is even.
Case 1: First Die is Even
If the first die is even, there are 3 possible outcomes for the second die (odd numbers) and 6 possible outcomes for the third die (any number). Therefore, there are 3 * 6 = 18 favorable outcomes for this case.
Case 2: First Die is Odd
If the first die is odd, there are 3 possible outcomes for the second die (odd numbers) and 6 possible outcomes for the third die (any number). Therefore, there are 3 * 6 = 18 favorable outcomes for this case.
Total Favorable Outcomes
The total number of favorable outcomes is the sum of the favorable outcomes for each case, which is 18 + 18 = 36.
Probability
The probability of getting a sum of the numbers on the three dice to be even, given that the number on the second die is odd, is the ratio of the number of favorable outcomes to the total number of possible outcomes.
Probability = Favorable Outcomes / Total Possible Outcomes
Probability = 36 / 108
Probability = 1/3
Therefore, the correct answer is option C) 1/3.
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Three dice are thrown together. What is the probability of getting sum of the numbers on the three dice to be even when it is known that number which appeared on the second die was odd?a)1/4b)1/2c)1/3d)2/3e)None of theseCorrect answer is option 'B'. Can you explain this answer?
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