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Three fair cubical dice are thrown simultaneously. The probability that all three dice have the same number of dots on the faces showing up is (up to third decimal place) __________.
Correct answer is between '0.027,0.028'. Can you explain this answer?
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Three fair cubical dice are thrown simultaneously. The probability tha...
The probability of one dot showing up in all the three = 1/6 x 1/6 x 1/6 = 1/216
The probability that two dots show up in all the three = 1/6 x/1/6 x 1/6 = 1/216
This probability is the same for 3, 4 , 5 and 6 dots;
So, the probability that the same number shows up in all the three dice
= 1/216 x 6 = 1/36 = 0.028 to the third decimal place
Most Upvoted Answer
Three fair cubical dice are thrown simultaneously. The probability tha...
Introduction:
The problem requires finding the probability that all three dice have the same number of dots on the faces showing up. Since each dice has six faces numbered from 1 to 6, there are a total of 6^3 = 216 possible outcomes.
Approach:
To find the probability, we need to determine the number of favorable outcomes (where all three dice have the same number of dots) and divide it by the total number of possible outcomes.
Favorable Outcomes:
There are six possible outcomes where all three dice have the same number of dots on the faces showing up: (1, 1, 1), (2, 2, 2), (3, 3, 3), (4, 4, 4), (5, 5, 5), and (6, 6, 6).
Total Outcomes:
As mentioned earlier, there are 216 possible outcomes when three dice are thrown simultaneously.
Probability Calculation:
To find the probability, we divide the number of favorable outcomes by the total number of possible outcomes:
Probability = (Number of Favorable Outcomes) / (Total Number of Outcomes)
Probability = 6 / 216
Probability ≈ 0.0278 (rounded to the nearest thousandth)
Conclusion:
The probability that all three dice have the same number of dots on the faces showing up is approximately 0.0278.
The problem requires finding the probability that all three dice have the same number of dots on the faces showing up. Since each dice has six faces numbered from 1 to 6, there are a total of 6^3 = 216 possible outcomes.
Approach:
To find the probability, we need to determine the number of favorable outcomes (where all three dice have the same number of dots) and divide it by the total number of possible outcomes.
Favorable Outcomes:
There are six possible outcomes where all three dice have the same number of dots on the faces showing up: (1, 1, 1), (2, 2, 2), (3, 3, 3), (4, 4, 4), (5, 5, 5), and (6, 6, 6).
Total Outcomes:
As mentioned earlier, there are 216 possible outcomes when three dice are thrown simultaneously.
Probability Calculation:
To find the probability, we divide the number of favorable outcomes by the total number of possible outcomes:
Probability = (Number of Favorable Outcomes) / (Total Number of Outcomes)
Probability = 6 / 216
Probability ≈ 0.0278 (rounded to the nearest thousandth)
Conclusion:
The probability that all three dice have the same number of dots on the faces showing up is approximately 0.0278.
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Three fair cubical dice are thrown simultaneously. The probability that all three dice have the same number of dots on the faces showing up is (up to third decimal place) __________.Correct answer is between '0.027,0.028'. Can you explain this answer?
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