# Ex.15.1 Q9 Probability Solution - NCERT Maths Class 10

## Question

A box contains \(5\) red marbles, \(8\) white marbles and \(4\) green marbles. One marble is taken out of the box at random. What is the probability that the marble taken out will be

(i) red?

(ii) white?

(iii) not green?

## Text Solution

**What is known?**

A box contains \(5\) red marbles, \(8\) white marbles and \(4\) green marbles. One marble is taken out of the box at random.

**What is unknown?**

The probability that the marble taken out will be (i) red? (ii) white? (iii) not green?

**Reasoning:**

This question can be solved easily;

(i) Find out the probability of getting red, white and green marble by using the formula

Probability of an event

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

(ii) Then by using the formula of sum of complementary event find out the probability of not getting green ball i.e. \(P\,(E) +P\) (not \(E\)) = 1.

**Steps:**

No of red balls in a bag \(=5\)

No of white balls in a bag \(=8\)

No of green balls in a bag \(=4 \)

Total no of balls \(= 5+8+ 4 =17\)

Probability of drawing red ball\(\begin{align}=\frac{5}{17}\end{align}\)

Probability of drawing white ball\(\begin{align}=\frac{8}{17}\end{align}\)

Probability of drawing a ball which is green\(\begin{align}=\frac{4}{17}\end{align}\)

\[\begin{align} P(\text{not }E) & =1- P(E) \\ {} & =1-\frac{4}{17} \\ & =\frac{13}{17} \\\end{align}\]