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When three dice are rolled simultaneously the probability that the number on the third die is greater than the sum of the numbers on two dice is
(a)12/216
(b)36/216
(c)48/216
(d)60/216?
(a)12/216
(b)36/216
(c)48/216
(d)60/216?
Most Upvoted Answer
When three dice are rolled simultaneously the probability that the num...
Calculating the Probability
To find the probability that the number on the third die is greater than the sum of the numbers on the first two dice, we need to first determine the total number of outcomes when three dice are rolled simultaneously.
Total Number of Outcomes
When a single die is rolled, there are 6 possible outcomes (1, 2, 3, 4, 5, 6). Since we are rolling three dice simultaneously, the total number of outcomes is 6 x 6 x 6 = 216.
Favorable Outcomes
For the third die to have a number greater than the sum of the numbers on the first two dice, we need to consider the possible combinations of outcomes on the first two dice.
When the first two dice show numbers (1, 1), the third die can have numbers (2, 3, 4, 5, 6), which gives us 5 favorable outcomes.
Similarly, for each combination of outcomes on the first two dice, we can calculate the number of favorable outcomes for the third die.
Calculating the Probability
The total number of favorable outcomes is the sum of favorable outcomes for all combinations of outcomes on the first two dice.
After calculating the total number of favorable outcomes, we can divide it by the total number of outcomes to find the probability.
Answer
The probability that the number on the third die is greater than the sum of the numbers on the first two dice is 60/216, which simplifies to 5/18.
Therefore, the correct answer is (d) 60/216.
To find the probability that the number on the third die is greater than the sum of the numbers on the first two dice, we need to first determine the total number of outcomes when three dice are rolled simultaneously.
Total Number of Outcomes
When a single die is rolled, there are 6 possible outcomes (1, 2, 3, 4, 5, 6). Since we are rolling three dice simultaneously, the total number of outcomes is 6 x 6 x 6 = 216.
Favorable Outcomes
For the third die to have a number greater than the sum of the numbers on the first two dice, we need to consider the possible combinations of outcomes on the first two dice.
When the first two dice show numbers (1, 1), the third die can have numbers (2, 3, 4, 5, 6), which gives us 5 favorable outcomes.
Similarly, for each combination of outcomes on the first two dice, we can calculate the number of favorable outcomes for the third die.
Calculating the Probability
The total number of favorable outcomes is the sum of favorable outcomes for all combinations of outcomes on the first two dice.
After calculating the total number of favorable outcomes, we can divide it by the total number of outcomes to find the probability.
Answer
The probability that the number on the third die is greater than the sum of the numbers on the first two dice is 60/216, which simplifies to 5/18.
Therefore, the correct answer is (d) 60/216.
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When three dice are rolled simultaneously the probability that the number on the third die is greater than the sum of the numbers on two dice is (a)12/216(b)36/216(c)48/216(d)60/216?
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When three dice are rolled simultaneously the probability that the number on the third die is greater than the sum of the numbers on two dice is (a)12/216(b)36/216(c)48/216(d)60/216? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about When three dice are rolled simultaneously the probability that the number on the third die is greater than the sum of the numbers on two dice is (a)12/216(b)36/216(c)48/216(d)60/216? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for When three dice are rolled simultaneously the probability that the number on the third die is greater than the sum of the numbers on two dice is (a)12/216(b)36/216(c)48/216(d)60/216?.
When three dice are rolled simultaneously the probability that the number on the third die is greater than the sum of the numbers on two dice is (a)12/216(b)36/216(c)48/216(d)60/216? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about When three dice are rolled simultaneously the probability that the number on the third die is greater than the sum of the numbers on two dice is (a)12/216(b)36/216(c)48/216(d)60/216? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for When three dice are rolled simultaneously the probability that the number on the third die is greater than the sum of the numbers on two dice is (a)12/216(b)36/216(c)48/216(d)60/216?.
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