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When 3 dice are rolled simultaneously the probability of a number on the third die is greater that the sum of the number on two dice is?
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Probability of a number on the third die being greater than the sum of the numbers on two dice
To find the probability of a number on the third die being greater than the sum of the numbers on two dice, we need to consider all the possible outcomes and determine the favorable outcomes.
Understanding the problem
- We have 3 dice, each with 6 faces numbered from 1 to 6.
- When we roll these 3 dice simultaneously, we get a random number on each die.
- We need to find the probability of the number on the third die being greater than the sum of the numbers on the other two dice.
Determining the sample space
The sample space is the set of all possible outcomes. In this case, each die has 6 possible outcomes, so the sample space for rolling 3 dice is 6 * 6 * 6 = 216.
Calculating favorable outcomes
To determine the favorable outcomes, we need to consider the different cases where the number on the third die is greater than the sum of the numbers on the other two dice.
Case 1: Sum of two dice is 2
- The only possible way to get a sum of 2 is by rolling a 1 on each of the two dice.
- In this case, the number on the third die can be any number from 1 to 6.
- So, there are 6 favorable outcomes for this case.
Case 2: Sum of two dice is 3
- The possible ways to get a sum of 3 are (1, 2) and (2, 1).
- In both these cases, the number on the third die can be any number from 1 to 6.
- So, there are 12 favorable outcomes for this case.
Similarly, we can calculate the favorable outcomes for each possible sum (ranging from 4 to 12) of the two dice.
Calculating the probability
To find the probability, we divide the number of favorable outcomes by the total number of possible outcomes (sample space).
- Total number of favorable outcomes = Sum of the favorable outcomes for each possible sum.
- Total number of possible outcomes = 216 (as calculated earlier).
Finally, we can calculate the probability by dividing the total number of favorable outcomes by the total number of possible outcomes.
Conclusion
The probability of a number on the third die being greater than the sum of the numbers on two dice can be determined by calculating the total number of favorable outcomes and dividing it by the total number of possible outcomes. The favorable outcomes can be determined by considering all the different cases where the sum of the two dice ranges from 2 to 12.
To find the probability of a number on the third die being greater than the sum of the numbers on two dice, we need to consider all the possible outcomes and determine the favorable outcomes.
Understanding the problem
- We have 3 dice, each with 6 faces numbered from 1 to 6.
- When we roll these 3 dice simultaneously, we get a random number on each die.
- We need to find the probability of the number on the third die being greater than the sum of the numbers on the other two dice.
Determining the sample space
The sample space is the set of all possible outcomes. In this case, each die has 6 possible outcomes, so the sample space for rolling 3 dice is 6 * 6 * 6 = 216.
Calculating favorable outcomes
To determine the favorable outcomes, we need to consider the different cases where the number on the third die is greater than the sum of the numbers on the other two dice.
Case 1: Sum of two dice is 2
- The only possible way to get a sum of 2 is by rolling a 1 on each of the two dice.
- In this case, the number on the third die can be any number from 1 to 6.
- So, there are 6 favorable outcomes for this case.
Case 2: Sum of two dice is 3
- The possible ways to get a sum of 3 are (1, 2) and (2, 1).
- In both these cases, the number on the third die can be any number from 1 to 6.
- So, there are 12 favorable outcomes for this case.
Similarly, we can calculate the favorable outcomes for each possible sum (ranging from 4 to 12) of the two dice.
Calculating the probability
To find the probability, we divide the number of favorable outcomes by the total number of possible outcomes (sample space).
- Total number of favorable outcomes = Sum of the favorable outcomes for each possible sum.
- Total number of possible outcomes = 216 (as calculated earlier).
Finally, we can calculate the probability by dividing the total number of favorable outcomes by the total number of possible outcomes.
Conclusion
The probability of a number on the third die being greater than the sum of the numbers on two dice can be determined by calculating the total number of favorable outcomes and dividing it by the total number of possible outcomes. The favorable outcomes can be determined by considering all the different cases where the sum of the two dice ranges from 2 to 12.
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When 3 dice are rolled simultaneously the probability of a number on the third die is greater that the sum of the number on two dice is?
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When 3 dice are rolled simultaneously the probability of a number on the third die is greater that the sum of the number on two dice is? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about When 3 dice are rolled simultaneously the probability of a number on the third die is greater that the sum of the number on two dice is? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for When 3 dice are rolled simultaneously the probability of a number on the third die is greater that the sum of the number on two dice is?.
When 3 dice are rolled simultaneously the probability of a number on the third die is greater that the sum of the number on two dice is? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about When 3 dice are rolled simultaneously the probability of a number on the third die is greater that the sum of the number on two dice is? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for When 3 dice are rolled simultaneously the probability of a number on the third die is greater that the sum of the number on two dice is?.
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