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Published on: 22/10/2025
Download CBSE Class 10th Standard CBSE Maths question papers, sample papers, important questions, and previous year solved papers in PDF format. Get free study materials, NCERT solutions, and exam preparation resources for Class 10th Standard CBSE Maths
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1.
A bag contains white, black and red balls only. A ball is drawn at random from the bag. The probability of getting a white ball is \(\frac{3}{10}\) and that of a black ball is \(\frac{2}{5}\) . Find the probability of getting a red ball. If the bag contains 20 black balls, then find the total number of balls in the bag.
2.
All the three face cards of spades are removed from a well-shuffled pack of 52 cards. A card is then drawn at random from the remaining pack. Find the probability of getting
(i) a spade
3.
A card is drawn at random from a well shuffled deck of playing cards.Find the probability that the card drawn is:
(i)A card of spade or an ace
(ii)A black king
(iii)Neither a jack nor a king
(iv)Either a king or a queen
4.
19 cards numbered 1,2,3,.....,19 are put in a box and mixed thoroughly.One person draws one card from the box.Find the probability that the number on the card is:
(i)even
(ii)A prime
(iii)Divisible by 3
(iv)Divisible by 3 and 2 both
5.
Gugu throws a die.What is the probability that she shows:
(i)an odd number
(ii)a number less than 5
(iii)a '6'
(iv)a prime number
(v)a number greater than 2?
6.
A letter is at drawn at random from the word 'MATHEMATICS'.Find the probability of drawing each of the different letters in the given word.
1.
Balls in the bag are of colours white, black and red.
Given, probability of getting a white ball = \(\frac{3}{10}\)
Probability of getting a black ball = \(\frac{2}{5}\)
Clearly, probability of getting a red ball = 1 - [ P(white ball) + P (black ball)]
\(\because \) [ sum of probabilities of all elementary event is 1]
= 1 - \(\frac{3}{10}\) - \(\frac{2}{5}\)
= \(\frac { 10-3-4 }{ 10 } =\frac { 3 }{ 10 } \)
Now, let the number of balls in the bag be x.
Since, it is given that, the number of black balls in the bag is 20.
\(\therefore \) Probability of getting a black ball = \(\frac { 20 }{ x } \)
\(\Rightarrow \quad \frac { 2 }{ 5 } =\frac { 20 }{ x } \)
\(\Rightarrow \quad x=50\)
Hence, the total number of balls in the bag = 50
2.
Remaining cards of spade=13-3=10
So, favourable outcomes=10,
i.e. n(E4)=10
∴ P(getting a spade)\(=\frac { 10 }{ 49 } \)
3.
\((i){4\over13}(ii){1\over26}(iii){11\over13}(iv){2\over13}\)
4.
\((i){9\over19}(ii){1\over19}(iii){6\over19}(iv){3\over19}\)
5.
\((i){1\over2}(ii){2\over3}(iii){1\over6}(iv){1\over2}(v){2\over3}\)
6.
\({2\over11},{2\over11},{2\over11},{1\over11},{1\over11},{1\over11},{1\over11},{1\over11}\)
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