If you roll a fair $6$-sided die, what is the probability of the complement of the event $“$rolling a number less than $5$$”$?

• A. $\frac{1}{3}$
• B. $\frac{1}{2}$
• C. $\frac{5}{6}$
• D. $\frac{2}{3}$

Answer: (A)

Verified step by step guidance

1. Identify the event of interest: rolling a number less than 5 on a six-sided die. The possible outcomes for this event are {1, 2, 3, 4}.
2. Calculate the probability of the event 'rolling a number less than 5'. Since the die is fair, each outcome has a probability of \( \frac{1}{6} \). The event has 4 favorable outcomes, so the probability is \( P(E) = \frac{4}{6} \).
3. Understand that the complement of an event \( E \) is the event that \( E \) does not occur. The complement of 'rolling a number less than 5' is 'rolling a number greater than or equal to 5'.
4. Use the complement rule, which states that \( P(E^c) = 1 - P(E) \), where \( E^c \) is the complement of event \( E \).
5. Substitute the value of \( P(E) \) into the complement rule to find \( P(E^c) = 1 - \frac{4}{6} \). Simplify this expression to get the probability of the complement event.