# Ex.15.1 Q16 Probability Solution - NCERT Maths Class 10

## Question

\(12\) defective pens are accidentally mixed with \(132\) good ones. It is not possible to just look at a pen and tell whether or not it is defective. One pen is taken out at random from this lot. Determine the probability that the pen taken out is a good one.

## Text Solution

**What is known?**

\(12\) defective pens are accidentally mixed with \(132\) good ones.

Total number of outcomes = \(144\)

**What is unknown?**

The probability of getting a good pen when \(1\) pen is picked randomly from the lot.

**Reasoning:**

This question can be solved easily by using the formula

Probability of an event

\[=\frac{\begin{bmatrix} \text { Number of}\\ \text{ possible outcomes }\end{bmatrix} }{ \begin{bmatrix}\text { Total no of} \\ \text{favorable outcomes} \end{bmatrix} }\]

**Steps:**

No of defective pens \(= 12\)

No of good pens \(= 132\)

Total no of pens

\(=12+132\\ =144\)

Probability that the pen taken out is a good one

\[\begin{align}& =\frac{\begin{bmatrix} \text { Number of}\\ \text{ possible outcomes }\end{bmatrix} }{ \begin{bmatrix}\text { Total no of} \\ \text{favorable outcomes} \end{bmatrix} } \\ &=\frac{132}{144} \\ &=\frac{11}{12} \\\end{align}\]

Thus, the probability that the pen taken out is a good \( = \frac{11}{12}\)