A standard die is rolled. Find the probability that the number rolled is less than 6 . Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Answer
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Step 1 ：A standard die has 6 faces, numbered 1 through 6. The question asks for the probability that the number rolled is less than 6. This means we are interested in the outcomes where the die shows 1, 2, 3, 4, or 5. There are 5 such outcomes. The total number of possible outcomes when rolling a die is 6.

Step 2 ：So, the probability of rolling a number less than 6 is the number of favorable outcomes divided by the total number of outcomes.

Step 3 ：Let's denote the number of favorable outcomes as \(f\) and the total number of outcomes as \(t\). In this case, \(f = 5\) and \(t = 6\).

Step 4 ：The probability \(p\) is then given by the formula \(p = \frac{f}{t}\). Substituting the given values, we get \(p = \frac{5}{6}\).

Step 5 ：Calculating the above expression, we get \(p = 0.8333333333333334\).

Step 6 ：Rounding to the nearest millionth, we get \(p = 0.833\).

Step 7 ：Final Answer: The probability that the number rolled is less than 6 is approximately \(\boxed{0.833}\).