In the verge of coronavirus pandemic, we are providing FREE access to our entire Online Curriculum to ensure Learning Doesn't STOP!

# Ex.15.1 Q18 Probability Solution - NCERT Maths Class 10

Go back to  'Ex.15.1'

## Question

A box contains $$90$$ discs which are numbered from $$1$$ to $$90$$. If one disc is drawn at random from the box, find the probability that it bears

(i) a two-digit number

(ii) a perfect square number

(iii) a number divisible by $$5$$.

Video Solution
Probability
Ex 15.1 | Question 18

## Text Solution

What is known?

Total number of discs = $$90$$

Total number of 2digit numbers between $$1$$ to $$90$$ = $$81$$

Total number of perfect square numbers between $$1$$ to $$90$$ are $$1,4,9,16,25,36,49,64,81= 9$$

Total numbers that are divisible by $$5$$ are $$5$$,$$10$$,$$15$$,$$20$$,$$25$$,$$30$$,$$35$$,$$40$$,$$45$$,$$50$$,$$55$$,$$60$$,$$65$$,$$70$$,$$75$$,$$80$$,$$85$$,$$90$$$$=18$$

What is unknown?

The probability that the disc bears

(i) a two-digit number

(ii) a perfect square number

(iii) a number divisible by $$5$$.

Steps:

(i) Probability of getting a two digit number

\begin{align}& =\frac{\begin{bmatrix} \text { Number of}\\ \text{ possible outcomes }\end{bmatrix} }{ \begin{bmatrix}\text { Total no of} \\ \text{favorabl outcomes} \end{bmatrix} } \\& =\frac{81}{90}\\&=\frac{9}{10} \end{align}

(ii) Probability of getting a perfect square number

\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{9}{90}\\&=\frac{1}{10} \end{align}

(iii) Probability of getting a number divisible by $$5$$

\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{18}{90} \\ & =\frac{1}{5} \end{align}

Learn from the best math teachers and top your exams

• Live one on one classroom and doubt clearing
• Practice worksheets in and after class for conceptual clarity
• Personalized curriculum to keep up with school