In a box of 100 transistors, 20 are defective. If event A is selecting a defective transistor, what is P(A)?
Understand the Problem
The question is asking for the probability of selecting a defective transistor from a box of 100 transistors, where 20 of them are defective. To find the probability P(A), we will use the formula for probability: P(A) = number of favorable outcomes / total outcomes.
Answer
$P(A) = \frac{1}{5}$ or $0.2$ or $20\%$
Answer for screen readers
$P(A) = \frac{1}{5}$ or $0.2$ or $20%$
Steps to Solve
- Identify the total number of outcomes
The total number of transistors in the box is 100.
- Identify the number of favorable outcomes
The number of defective transistors, which are our favorable outcomes, is 20.
- Use the probability formula
We apply the probability formula:
$$ P(A) = \frac{\text{number of favorable outcomes}}{\text{total outcomes}} $$
Substituting in the values:
$$ P(A) = \frac{20}{100} $$
- Simplify the probability
Simplifying the fraction gives:
$$ P(A) = \frac{1}{5} $$
- Convert to decimal or percentage if needed
If required, we can also express this as a decimal:
$$ P(A) = 0.2 $$
Or as a percentage:
$$ P(A) = 20% $$
$P(A) = \frac{1}{5}$ or $0.2$ or $20%$
More Information
The probability of selecting a defective transistor is 20%. Understanding probability is crucial in various real-life applications, such as quality control and risk assessment.
Tips
- Failing to correctly identify the total number of outcomes.
- Forgetting to simplify the probability fraction.
- Not expressing the answer in the required format (fraction, decimal or percentage).
AI-generated content may contain errors. Please verify critical information
