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What is the Probability of Failure?
Grade Level:
Class 12
AI/ML, Physics, Biotechnology, FinTech, EVs, Space Technology, Climate Science, Blockchain, Medicine, Engineering, Law, Economics
Definition
What is it?
The Probability of Failure is the chance or likelihood that an event will NOT happen. It measures how often we expect something to go wrong, or not achieve its intended outcome. It's simply 1 minus the probability of success.
Simple Example
Quick Example
Imagine your favourite cricket team plays 10 matches, and they win 7 of them. The probability of them winning is 7/10. So, the probability of them *failing* to win (losing or drawing) is 1 - 7/10 = 3/10.
Worked Example
Step-by-Step
Let's say a local bakery makes 50 cakes every day. Out of these, 5 cakes usually get burnt or spoiled.
Step 1: Identify the total number of trials. Total cakes made = 50.
---Step 2: Identify the number of 'failure' events. Number of spoiled cakes = 5.
---Step 3: Calculate the probability of failure. Probability of Failure = (Number of failure events) / (Total number of trials).
---Step 4: Substitute the values. Probability of Failure = 5 / 50.
---Step 5: Simplify the fraction. Probability of Failure = 1 / 10.
---Step 6: Convert to decimal or percentage if needed. Probability of Failure = 0.1 or 10%.
Answer: The probability of a cake failing (being spoiled) is 1/10 or 10%.
Why It Matters
Understanding the probability of failure is crucial in many fields, from designing safe rockets at ISRO to predicting stock market crashes in FinTech. Engineers use it to build stronger bridges, doctors use it to assess treatment risks, and AI/ML experts use it to improve prediction models. It helps us make better decisions and prepare for challenges.
Common Mistakes
MISTAKE: Confusing probability of failure with probability of success. | CORRECTION: Remember that P(Failure) = 1 - P(Success). If you know one, you can always find the other.
MISTAKE: Forgetting to simplify the fraction. | CORRECTION: Always simplify your probability fractions to their lowest terms (e.g., 5/50 should be 1/10) for clarity.
MISTAKE: Using the wrong total number of outcomes in the denominator. | CORRECTION: Ensure the denominator is the *total* number of all possible outcomes, not just the successful ones or the failed ones.
Practice Questions
Try It Yourself
QUESTION: A traffic light at a busy junction works correctly 9 out of 10 times. What is the probability of it failing to work correctly? | ANSWER: 1/10 or 0.1
QUESTION: In a batch of 20 mobile phones, 3 are found to have a manufacturing defect. What is the probability that a randomly chosen phone from this batch will have a defect (i.e., be a 'failure')? | ANSWER: 3/20 or 0.15
QUESTION: A student takes a multiple-choice test with 5 questions. For each question, there are 4 options, and only one is correct. If the student guesses randomly for one question, what is the probability of them failing to answer it correctly? | ANSWER: 3/4 or 0.75
MCQ
Quick Quiz
If the probability of a new electric scooter starting successfully is 0.95, what is the probability of it failing to start?
0.05
0.95
1
The Correct Answer Is:
A
The probability of failure is 1 minus the probability of success. So, 1 - 0.95 = 0.05. Options B, C, and D are incorrect calculations or represent success/certainty/impossibility.
Real World Connection
In the Real World
When you book a cab using an app like Ola or Uber, the app's developers calculate the probability of a ride being cancelled or a driver not showing up. This helps them improve their service, like suggesting alternative drivers or offering discounts, to reduce 'failure' events and keep customers happy.
Key Vocabulary
Key Terms
PROBABILITY: The chance of an event happening | SUCCESS: When an event achieves its desired outcome | FAILURE: When an event does NOT achieve its desired outcome | OUTCOME: A possible result of an experiment or event | TRIAL: A single instance of an experiment or event
What's Next
What to Learn Next
Great job understanding the basics of probability! Next, you can explore 'Conditional Probability' to see how the chance of an event changes if another event has already happened. This builds directly on what you've learned here and opens doors to even more exciting applications!
