# Ex.15.1 Q17 Probability Solution - NCERT Maths Class 10

## Question

(i) A lot of \(20\) bulbs contain \(4\) defective ones. One bulb is drawn at random from the lot. What is the probability that this bulb is defective?

(ii) Suppose the bulb drawn in is not defective and is not replaced. Now one bulb is drawn at random from the rest. What is the probability that this bulb is not defective?

## Text Solution

**What is known?**

A lot of \(20\) bulbs contain \(4\) defective ones. One bulb is drawn at random from the lot.

**What is unknown?**

The probability of getting a defective bulb when \(1\) bulb is drawn 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:**

Total no of bulbs = \(20\)

No of defective pieces = \(4\)

Probability that this bulb is defective

\[\begin{align}& =\frac{\begin{bmatrix} \text { Number of}\\ \text{ possible outcomes }\end{bmatrix} }{ \begin{bmatrix}\text { Total no of} \\ \text{favorable outcomes} \end{bmatrix} } \\&=\frac{4}{20} \\ &=\frac{1}{5} \\\end{align}\]

Remaining total number of bulbs\(=\text{ }20-1=19\)

Remaining total number of non-defective bulbs \(=16-1=15\)

Probability that this bulb is not defective

\[\begin{align}& =\frac{\begin{bmatrix} \text { Number of}\\ \text{ possible outcomes }\end{bmatrix} }{ \begin{bmatrix}\text { Total no of} \\ \text{favorable outcomes} \end{bmatrix} } \\& =\frac{15}{19} \end{align}\]