Questions: HW Empirical and Theoretical Probability Question 6 of 18 (1 point) Question Attempt: 1 of 3 Express the answers in simplest form. If a die is rolled one time, find the probability of Part: 0 / 5 Part 1 of 5 (a) Getting a 4. P(4)=

Solution Steps

To find the probability of rolling a specific number on a fair six-sided die, we need to consider the total number of possible outcomes and the number of favorable outcomes. Since a die has six faces, the total number of outcomes is 6. The favorable outcome for rolling a 4 is just one (rolling a 4 itself). Therefore, the probability is the ratio of favorable outcomes to the total number of outcomes.

When rolling a fair six-sided die, the total number of possible outcomes is given by the number of faces on the die, which is \( 6 \).

The favorable outcome for this problem is rolling a \( 4 \). There is only one way to achieve this outcome, so the number of favorable outcomes is \( 1 \).

The probability \( P(4) \) of rolling a \( 4 \) can be calculated using the formula: \[ P(4) = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Outcomes}} = \frac{1}{6} \] This evaluates to approximately \( 0.1667 \) when expressed as a decimal.

Final Answer