Scenario: Weather & Decision Making - Learn to apply probability to real-world situations and decision making!
You're planning a school picnic for tomorrow. The weather forecast says there's a 30% chance of rain. You need to decide whether to hold the picnic outdoors or move it indoors. The outdoor venue is free, but the indoor venue costs $200. If it rains and you're outdoors, you'll lose $150 in wasted food and setup.
Decision Challenge:
Use probability to make the best decision about where to hold the picnic.
Option 1: Outdoor Picnic
Option 2: Indoor Picnic
Expected Value: The average outcome you can expect over many similar decisions.
Formula: Expected Value = (Probability × Outcome) + (Probability × Outcome) + ...
Option 1: Outdoor Picnic
Rain (30%): 0.30 × (-$150) = -$45
No Rain (70%): 0.70 × $0 = $0
Expected Value: -$45 + $0 = -$45
Option 2: Indoor Picnic
Rain (30%): 0.30 × $200 = $60
No Rain (70%): 0.70 × $200 = $140
Expected Value: $60 + $140 = $200
Outdoor Expected Value: -$45 (average loss)
Indoor Expected Value: $200 (guaranteed cost)
Recommendation: Choose outdoor picnic because the expected loss (-$45) is less than the guaranteed cost of indoor ($200).
Weather Probability: The chance that a specific weather event will occur in a given area during a specific time period.
Example: "30% chance of rain" means that in 100 similar weather situations, it would rain in about 30 of them.
Farmers use rain probability to decide when to plant crops or apply pesticides.
Event organizers use weather probability to plan outdoor activities and backup options.
Airlines and shipping companies use weather probability for route planning.
Insurance companies use weather probability to set premiums and assess risk.
Risk Assessment: The process of evaluating the potential for loss or harm based on probability and impact.
Risk = Probability × Impact
You're considering investing $1,000 in a stock. There's a 20% chance it will double in value and an 80% chance it will lose half its value.
Scenario 1 (20% chance): Stock doubles → Gain $1,000
Scenario 2 (80% chance): Stock loses half → Lose $500
Expected Value: (0.20 × $1,000) + (0.80 × -$500) = $200 - $400 = -$200
Risk Assessment: Expected loss of $200 suggests this is a risky investment.
You're planning a beach day. There's a 40% chance of rain. If it rains, you'll waste $50 on gas and food. If you stay home, you'll save the $50 but miss the fun. What should you do?
Your analysis:
In a game show, you can either take $500 guaranteed or spin a wheel with a 25% chance of winning $2,000 and a 75% chance of winning nothing. Which option should you choose?
Your decision: