Probability in Finance and Life

Making Smart Decisions with Math Year 10 Mathematics Real-World Applications

What is Probability?

The likelihood that an event will occur Expressed as a fraction, decimal, or percentage Ranges from 0 (impossible) to 1 (certain) Formula: P(event) = favorable outcomes / total outcomes

Quick Probability Check

What's the probability of rolling a 6 on a fair die? What's the probability of drawing a red card from a standard deck? What's the probability of it raining if there's a 30% chance?

Probability in Insurance

Insurance companies use probability to set premiums They calculate risk based on historical data Young drivers pay more due to higher accident probability Life expectancy tables determine life insurance costs

Investment Risk vs. Return

{"left":"Low Risk: Savings accounts, government bonds, CDs\nHigh Risk: Stocks, cryptocurrency, startup investments","right":"Higher probability of loss = Higher potential returns\nDiversification reduces overall risk"}

Real-Life Scenario

You have $1,000 to invest. Option A: 100% chance of 2% return. Option B: 50% chance of 8% return, 50% chance of losing 2%. Which would you choose and why? Calculate the expected value for each option.

Credit and Loan Probability

Credit scores predict probability of loan repayment Higher credit score = lower interest rates Banks use probability models to approve loans Default risk affects lending decisions

Expected Value in Daily Decisions

Calculate Your Future

Scenario: College costs $40,000/year for 4 years With degree: 70% chance of $60,000/year job, 30% chance of $45,000/year job Without degree: 90% chance of $30,000/year job, 10% chance of $35,000/year job Calculate expected lifetime earnings for each path (assume 40-year career)

Key Takeaway

'In the business world, the rearview mirror is always clearer than the windshield.' - Warren Buffett Probability helps us make better decisions with uncertain futures Understanding risk and expected value guides smart financial choices