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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 '0.027 to 0.028'. Can you explain this answer?
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Three fair cubical dice are thrown simultaneously. The probability tha...
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Three fair cubical dice are thrown simultaneously. The probability tha...
Possible outcomes =6*6*6=216
Favourable outcomes =6 (when all dice are either 1-1-1, 2-2-2, 3-3-3,4-4-4,5-5-5,6-6-6)
Probabilty= 6/216= 0.027777
Favourable outcomes =6 (when all dice are either 1-1-1, 2-2-2, 3-3-3,4-4-4,5-5-5,6-6-6)
Probabilty= 6/216= 0.027777
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Three fair cubical dice are thrown simultaneously. The probability tha...
Problem: 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) __________.
Solution:
When three fair dice are thrown simultaneously, the total number of possible outcomes is $6^3 = 216$. Now, let us count the number of favorable outcomes where all three dice show the same number. There are six possible outcomes for the number on the first die. For each of these outcomes, there is only one favorable outcome where the same number appears on the remaining two dice. Therefore, there are a total of six favorable outcomes.
Hence, the probability that all three dice show the same number is given by:
$$P(\text{All three dice show the same number}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{6}{216} \approx \boxed{0.027\text{ to }0.028}$$
Conclusion: The probability that all three dice have the same number of dots on the faces showing up is approximately 0.027 to 0.028.
Solution:
When three fair dice are thrown simultaneously, the total number of possible outcomes is $6^3 = 216$. Now, let us count the number of favorable outcomes where all three dice show the same number. There are six possible outcomes for the number on the first die. For each of these outcomes, there is only one favorable outcome where the same number appears on the remaining two dice. Therefore, there are a total of six favorable outcomes.
Hence, the probability that all three dice show the same number is given by:
$$P(\text{All three dice show the same number}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{6}{216} \approx \boxed{0.027\text{ to }0.028}$$
Conclusion: The probability that all three dice have the same number of dots on the faces showing up is approximately 0.027 to 0.028.
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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 '0.027 to 0.028'. Can you explain this answer?
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