You have three dice: one red (R), one green (G), and one blue (B). When all three dice are rolled at the same time, how do you calculate the probability of the following outcomes: no sixes at all?
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To calculate the probability of no sixes when rolling all three dice, first determine the probability of not rolling a six on a single die. Since there are 6 possible outcomes on a die and only 1 outcome is a six, the probability of not rolling a six on one die is ( \frac{5}{6} ).
Since each die is independent of the others, you multiply the probabilities together. So, the probability of not rolling a six on all three dice is ( \frac{5}{6} \times \frac{5}{6} \times \frac{5}{6} ).
Calculate this expression to find the probability of no sixes at all.
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To calculate the probability of rolling no sixes at all with three dice (one red, one green, and one blue), you follow these steps:

First, determine the probability of not rolling a six with a single die. Since a die has 6 faces, and 5 of those faces are not a six, the probability of not rolling a six with one die is ( \frac{5}{6} ).

Since the dice are independent of each other, the probability of not rolling a six on any of the dice (R, G, B) simultaneously is the product of their individual probabilities. So, for all three dice, the probability is ( \left(\frac{5}{6}\right)^3 ).

Calculate this value: ( \left(\frac{5}{6}\right)^3 = \frac{125}{216} ).
Thus, the probability of rolling no sixes at all when rolling three dice simultaneously is ( \frac{125}{216} ).
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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