FAILURE

Failure

Definition Of Failure

Failure is any outcome other than the desired outcome.
For example, suppose you toss a coin and you want a head to show up.
But if a tail shows up, then it is called a failure.

Video Examples: iCoachMath works

Solved Example on Failure

Ques: On an average, there is rainfall on 12 days in every 31 days. To find the probability that it rains for 2 days every week, describe a trial (n) and a success (x) and find the probability of a failure (q).

Choices:

A. n = 7, x = 2, q = 0.39
B. n = 7, x = 2, q = 0.61
C. n = 2, x = 7, q = 0.39
D. n = 2, x = 7, q = 0.61
Correct Answer: B

Solution:

Step 1: The number of trials is the number of days in a week, so n = 7.
Step 2: If it rains, then it is a success. So, x = 2.
Step 3: The probability for a success,
p = 12/31 = 0.39. [p + q = 1.]
Step 4: q = 1 - p = 1 - 0.39 = 0.61

Quick Summary

Failure is the opposite of success in a probabilistic event.
The probability of failure is calculated by subtracting the probability of success from 1.
Understanding failure is crucial for calculating overall probabilities.

\[ P(Failure) = 1 - P(Success) \]

🍎 Teacher Insights

Emphasize the complementary relationship between success and failure. Use real-world examples, like weather forecasts, to illustrate the concept. Encourage students to identify successes and failures in various scenarios.

🎓 Prerequisites

Basic Arithmetic
Fractions
Understanding of Events

Check Your Knowledge

Q1: If the probability of success is 0.4, what is the probability of failure?

0.6 0.4 0.5 0.1

Q2: In a coin toss, if heads is considered a success, what is the failure?

Heads Tails The coin landing on its side None of the above

Frequently Asked Questions

Q: What does 'failure' mean in the context of probability?
A: In probability, 'failure' refers to any outcome that is not the desired or defined 'success'.

Q: How do you calculate the probability of failure?
A: The probability of failure is calculated as 1 minus the probability of success: P(Failure) = 1 - P(Success).