Addition Rule for Probabilities: Smarter Investment Decisions in 2026

The addition rule is a basic principle in probability theory that helps you calculate the chance that at least one of two or more events will happen. There are two main scenarios to consider:

Mutually Exclusive Events

These are events that cannot both occur at the same time. For example, if you draw a single card from a deck, it can’t be both a heart and a club. In finance, this could be like choosing between two exclusive investment options—if you pick one, you can’t pick the other in the same transaction.

Formula:

P(A or B) = P(A) + P(B)

Non-Mutually Exclusive Events

These are events that can overlap, meaning both can occur together. For example, two different investments in your portfolio could both perform well in the same period.

Formula:

P(A or B) = P(A) + P(B) – P(A and B)

The subtraction of P(A and B) ensures you don’t double-count the probability of both events happening together. This distinction is important in finance, where risks and opportunities often overlap.

Suppose you’re considering two Australian ETFs: one focused on technology, the other on sustainable energy. You want to estimate the probability that at least one will outperform the market in 2026. If you have the following estimates:

• Probability the tech ETF outperforms: 30%
• Probability the energy ETF outperforms: 25%
• Probability both outperform: 10%

Using the addition rule for non-mutually exclusive events:

P(Tech or Energy outperforms) = 0.30 + 0.25 – 0.10 = 0.45 (or 45%)

This calculation gives you a clearer sense of your chances of having at least one strong performer in your portfolio. It’s a practical way to assess diversification benefits and manage expectations.

Australia’s financial environment in 2026 is shaped by ongoing economic shifts, policy updates, and global uncertainty. Investors face a range of risks and opportunities that often overlap. The addition rule helps you:

• Assess Overlapping Risks: Many investments are affected by similar factors, such as interest rate changes or sector trends. The addition rule helps you avoid overestimating your chances by accounting for overlaps.
• Plan for Multiple Outcomes: Whether you’re considering the impact of regulatory changes, market volatility, or sector performance, the addition rule lets you estimate the likelihood of at least one event affecting your portfolio.
• Support Data-Driven Decisions: Rather than relying on intuition alone, you can use probability to guide your choices, especially when conditions are uncertain.

Interest Rate Sensitivity

If you hold investments sensitive to Reserve Bank of Australia (RBA) rate decisions, you can use the addition rule to estimate the chance that one or more holdings will be affected by a rate change. This helps you plan for potential impacts across your portfolio.

Insurance and Hedging

Risk management often involves considering multiple threats, such as market downturns or currency fluctuations. By applying the addition rule, you can estimate the likelihood that at least one risk will materialise, helping you decide whether insurance products or other hedging strategies are appropriate.

Policy and Regulatory Changes

With ongoing reforms to superannuation and taxation, it’s important to consider how likely it is that one or more policy changes will affect your investments. The addition rule helps you quantify these possibilities and prepare accordingly.

1. Use Reliable Data

Base your probability estimates on current, reputable sources. Avoid relying solely on past performance, as market conditions can change.

2. Identify Event Overlaps

Carefully consider whether the events you’re analysing can occur together. If they can, remember to subtract the probability of both happening to avoid overestimating your chances.

3. Leverage Financial Tools

Many portfolio management platforms include probability calculators or scenario analysis features. Use these tools to test your assumptions and explore different outcomes before making major decisions.

4. Run Scenario Analyses

Consider best-case, worst-case, and middle-ground scenarios using the addition rule. This approach helps you prepare for a range of possible futures, especially as economic and policy conditions evolve in 2026.

5. Review and Adjust Regularly

Probabilities can change as new information becomes available. Make it a habit to review your assumptions and update your calculations as needed.

While the addition rule is often discussed in the context of investing, it can also be useful in other areas of personal finance. For example, when considering different types of insurance coverage, you can use the rule to estimate the likelihood that at least one risk will require a claim. This can help you decide on the right level of cover for your needs.

Similarly, if you’re planning for major life events—such as buying a home, starting a business, or funding education—the addition rule can help you assess the probability that one or more factors will influence your plans. By quantifying these risks, you can make more confident, well-informed choices.

The addition rule for probabilities is a straightforward yet powerful concept that can enhance your financial decision-making in 2026. By understanding how to apply it—especially in situations where risks and opportunities overlap—you can better manage uncertainty, diversify your investments, and plan for a range of possible outcomes. Whether you’re building a portfolio, managing risk, or preparing for policy changes, using probability as a tool can help you move from guesswork to informed strategy.