What is Probability❓

### Probability = likelihood — possibility — chance of happening.

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### Probability distribution — gives possibility of each outcome of a random experiment — provides probabilities of different possible occurrences.

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### Applications in various sectors — make future predictions based on a sample for a random experiment — e.g. in business — predict if profit or loss to the company using any new strategy.

What is Expected Value (EV)❓

### Single weighted average ≡ long run average (mean) ≈ average result.

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### As if — same event (*x*) — take place repeatedly — thousands of times — ongoing basis — over a long run period of time.

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### As opposed to one-off situation — either 100% profit or 100% loss — where expected value (EV) may be misleading.

Be mindful ⚠

### ℹ Take note : actual ≠ expectation — therefore — expected value (EV) ≠ most likely outcome ≠ possible result — not to be mistaken.

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### ℹ Outcome — highest probability = most likely outcome = possible result.

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### ℹ Actual outcome — actual result — may below OR above EV (expectation).

How to measure EV❓

### ℹ Using formula.

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### ℹ Formula ▼

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### EV = ∑*px*

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### where :

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*p* = probability of the outcome occurring (chances of happening)

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*x* = future outcome e.g. cash flow $

What about risk profile of decision makers❓ Does it matter❓

### ℹ Yes — absolutely — different risk-return attitude — influence decision making outcome.

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### ℹ Risk profile :

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### 1️⃣ risk-taking person

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### 2️⃣ risk-avoiding person

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### 3️⃣ risk indifferent person – don’t bothering risk

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### ℹ Take risk — risk seeker — go for best possible outcomes (higher payoff) but less certainty — apply “Maximax” approach — high risk high return — bet the best outcome to happen.

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### ℹ Avoid risk — risk averse — go for lower possible outcome (lower payoff) but more certainty — apply “Maximin” or “Minimax” approach — low risk low return.

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### ℹ Don’t bother risk — risk neutral — indifferent in risk — only focus on return — regardless degree of risk — consider all possible outcomes — go for highest payoff.

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### ℹ Thought-provoking : Which one should be the priority concern?

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### 🤔 Risk? Return?

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### 🤔 Return then Risk?

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### 🤔 Risk then Return?

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### 🤔 Only Risk?

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### 🤔 Only Return?

What are the benefits of using expected values❓

### Some of the benefits | advantages :

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### ℹ Identify calculated risk — probability of each possible outcome — expected value.

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### ℹ Reduced information — easier decisions.

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### ℹ Calculations — relatively simple.

What are the limitations of expected values❓

### Some of the limitations | disadvantages :

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### ℹ Probabilities — subjective.

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### ℹ EV — merely a weighted average — little meaning for a one-off project.

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### ℹ EV gives no indication of the dispersion of possible outcomes about the EV, i.e. the risk.

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### ℹ EV – not correspond – not relatable – to any of the actual possible outcomes.

How Utility Theory influence decision making❓

### ℹ Risk attitude — depend on the amount of money involved — BIG deal [V.S] small deal.

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### ℹ Imagine two separate proposals ▼ which to accept or reject❓

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### 1️⃣ Bet on the toss of a coin — if heads — win $6 — otherwise — lose $4.

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### 2️⃣ Bet on the toss of a coin — if heads — win $6,000 — otherwise — lose $4,000.

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### ℹ For average person — scenario 2️⃣ riskier than 1️⃣ — due to BIG sums of money — no bother probabilities — ignoring range of possible outcomes — therefore might…

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### ✅ Accept 1️⃣

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### ❎ Reject 2️⃣