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 \( = \frac{11}{12}\)