To solve the question in the image:

Question:

A standard die is rolled. Find the probability that the number rolled is less than 4. Express your answer as a fraction in the lowest terms or as a decimal rounded to the nearest millionth.

Solution:

1. A standard die has 6 faces, numbered 1 through 6.
2. The event "number rolled is less than 4" includes the outcomes: 1, 2, and 3.
3. Total possible outcomes = 6.
4. Favorable outcomes (less than 4) = 3 (outcomes: 1, 2, 3).

The probability $P$ is calculated as: $P = \frac{\text{Favorable outcomes}}{\text{Total possible outcomes}} = \frac{3}{6} = \frac{1}{2}.$

Final Answer:

• Fraction: $\frac{1}{2}$
• Decimal: $0.5$

Let me know if you want further details or have any other questions!

5 Related Questions:

1. What is the probability of rolling an even number on a standard die?
2. What is the probability of rolling a number greater than or equal to 5?
3. If two dice are rolled, what is the probability their sum is less than 5?
4. How would the probability change if the die is biased towards certain numbers?
5. What is the probability of rolling a number less than 2?

Tip:

Always reduce probabilities to their simplest fraction form for clarity.