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

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## 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
$=\frac{\begin{Bmatrix} \text { Number of}\\ \text{ possible } \\ \text{outcomes }\end{Bmatrix} }{ \begin{Bmatrix}\text { Total no of} \\ \text{favorable} \\ \text{outcomes} \end{Bmatrix} }$

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 } \\ \text{outcomes }\end{Bmatrix} }{ \begin{Bmatrix}\text { Total no of} \\ \text{favorable} \\ \text{outcomes} \end{Bmatrix} } \\ &=\frac{132}{144} \\ &=\frac{11}{12} \\\end{align}

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

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