Questions: You roll a six-sided die. Find the probability of each of the following scenarios. (a) Rolling a 6 or a number greater than 3 (b) Rolling a number less than 4 or an even number (c) Rolling a 2 or an odd number (a) P(6 or number >3) = (Round to three decimal places as needed.)

Solution Steps

To solve these probability questions, we need to determine the favorable outcomes for each scenario and divide by the total number of possible outcomes (which is 6 for a six-sided die).

(a) For rolling a 6 or a number greater than 3, we identify the numbers that satisfy this condition and count them.

(b) For rolling a number less than 4 or an even number, we identify the numbers that satisfy either condition and count them.

(c) For rolling a 2 or an odd number, we identify the numbers that satisfy either condition and count them.

To find the probability of rolling a 6 or a number greater than 3, we identify the favorable outcomes: \( \{4, 5, 6\} \). The total number of outcomes when rolling a six-sided die is 6. Thus, the probability is calculated as:

\[ P(6 \text{ or } >3) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{3}{6} = 0.5 \]

Next, we calculate the probability of rolling a number less than 4 or an even number. The favorable outcomes are \( \{1, 2, 3, 4, 6\} \). Therefore, the probability is:

\[ P(<4 \text{ or even}) = \frac{5}{6} \approx 0.8333 \]

Finally, we find the probability of rolling a 2 or an odd number. The favorable outcomes are \( \{1, 2, 3, 5\} \). Thus, the probability is:

\[ P(2 \text{ or odd}) = \frac{4}{6} = \frac{2}{3} \approx 0.6667 \]

Final Answer