Which of the following situations requires the use of the $addition$ rule in probability?

• A. Calculating the probability of drawing two aces in a row from a deck without replacement
• B. Calculating the probability of drawing a $red$ card $\vee$ a $king$ from a standard deck of cards
• C. Calculating the probability of rolling a $4$ and then a $5$ on two dice
• D. Calculating the probability of getting heads on a single coin toss

Answer: (B)

Verified step by step guidance

1. Step 1: Understand the addition rule in probability. The addition rule is used when you want to find the probability of the occurrence of at least one of two events, often written as \(P(A \cup B)\), which means the probability of event A or event B happening.
2. Step 2: Recall the formula for the addition rule: \(P(A \cup B) = P(A) + P(B) - P(A \cap B)\), where \(P(A \cap B)\) is the probability that both events A and B occur simultaneously. This formula accounts for any overlap between the two events to avoid double counting.
3. Step 3: Analyze each situation to determine if it involves finding the probability of either one event or another (i.e., an "or" situation) or the probability of both events happening in sequence (an "and" situation).
4. Step 4: Recognize that "Calculating the probability of drawing a red card or a king from a standard deck of cards" is an "or" situation because you want the probability of either drawing a red card or drawing a king, which fits the addition rule scenario.
5. Step 5: Confirm that other options involve "and" situations (like drawing two aces in a row or rolling a 4 and then a 5) or a single event (like getting heads on a coin toss), which do not require the addition rule but rather multiplication or simple probability.