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Lesson 5-4: Probability Applications

Scenario: Weather Predictions - Apply probability concepts to make informed decisions about weather and events!

Duration: 65-80 minutesScenario: Weather Predictions

Learning Objectives

  • Apply probability concepts to real-world decision making
  • Use probability to make predictions and informed choices
  • Understand how probability affects daily life decisions
  • Solve complex probability problems with multiple steps

Weather Prediction Problem

Planning a School Picnic

Your school is planning a picnic next week. The weather forecast shows: - 30% chance of rain on Monday - 20% chance of rain on Tuesday - 40% chance of rain on Wednesday - 10% chance of rain on Thursday - 25% chance of rain on Friday

Questions:
1. Which day has the lowest chance of rain?
2. What is the probability that it will NOT rain on Thursday?
3. If you choose a day randomly, what's the probability of picking a day with less than 25% chance of rain?

M

30%

T

20%

W

40%

T

10%

F

25%

Rain probability by day

Step-by-Step Solutions

Question 1: Which day has the lowest chance of rain?

Compare all percentages: 30%, 20%, 40%, 10%, 25%
Thursday has 10% chance of rain - the lowest!

Question 2: Probability that it will NOT rain on Thursday

If P(rain) = 10% = 0.1
Then P(no rain) = 1 - P(rain) = 1 - 0.1 = 0.9 = 90%

Question 3: Probability of picking a day with less than 25% chance of rain

Days with less than 25% rain: Tuesday (20%) and Thursday (10%)
Favorable outcomes: 2 days
Total possible outcomes: 5 days
Probability = 2/5 = 0.4 = 40%

Recommendation: Thursday is the best day for the picnic with only 10% chance of rain!

Real-World Applications

Weather & Planning

  • • Planning outdoor events
  • • Deciding what to wear
  • • Agricultural planning
  • • Travel decisions

Example: 80% chance of rain means bring an umbrella!

Games & Entertainment

  • • Card games and board games
  • • Sports betting and odds
  • • Lottery and raffles
  • • Video game mechanics

Example: Understanding odds helps make better game decisions

Health & Safety

  • • Medical test results
  • • Safety equipment effectiveness
  • • Risk assessment
  • • Insurance decisions

Example: 95% effective vaccine means 5% chance of getting sick

Business & Finance

  • • Investment decisions
  • • Market predictions
  • • Quality control
  • • Risk management

Example: 70% chance of profit influences investment choices

Decision Making Process

How to Use Probability in Decisions

Step 1: Identify the Problem

What decision do you need to make? What are your options?

Step 2: Gather Information

Collect data and probabilities for each possible outcome.

Step 3: Calculate Probabilities

Use probability formulas to find the likelihood of each outcome.

Step 4: Make Your Decision

Choose the option with the best probability for your desired outcome.

Practice Problems

Problem 1

A restaurant has a 15% chance of running out of your favorite dish. What is the probability that they will have it available?

Your solution:

Problem 2

You're choosing between two routes to school. Route A has a 20% chance of traffic, Route B has a 35% chance of traffic. Which route should you choose and why?

Your reasoning: