Maths Class X Question Bank

Question 1 of 30

1. Question
1 point(s)
A fair coin is tossed thrice. Find the probability of getting.
(a) No heads
(b) at least one head.
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Hint

(i) P(at least one head) $=\dfrac{3}{4}$
(ii) P(no head) $=\dfrac{1}{4}$
Question 2 of 30

2. Question
1 point(s)
A box contains cards numbered from 1 to 17. If one card is drawn at random from the box, find the probability that it bears a prime number.
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Hint

Total chances = 17
Number of favourable chances = 7
$P(E)=\dfrac{7}{17}$
Question 3 of 30

3. Question
1 point(s)
From a deck of playing cards all spades are removed, a card is drawn at random from the remaining cards. Find the probability that it is a :
(a) red card
(b) black face card
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Hint

(i) P(red card) $=\dfrac{3}{49}$
(ii) Total cards $=52$
Total cards left $=40$
P(black face) $=\dfrac{3}{49}$
Question 4 of 30

4. Question
1 point(s)
A card is drawn at random from a well shuffled pack of 52 playing cards. Find the probability that card drawn is :
(a) spade or an ace
(b) neither king nor queen
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Hint

(i) Probability of the card drawn is a card of spade or ace
$=\dfrac{13}{52}+\dfrac{4}{52}-\dfrac{1}{52}=\dfrac{16}{52}=\dfrac{4}{13}$
(ii) P(neither king nor queen) $=1-\left(\dfrac{4+4}{52}\right)$
$=1-\dfrac{8}{52}=1-\dfrac{2}{13}=\dfrac{11}{13}$
Question 5 of 30

5. Question
1 point(s)
Form a deck of playing cards all aces and clubs are removed, a card is drawn at random from the remaining cards. Find the probability that it is :
(a) a black face card.
(b) a red card
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Hint

Remaining cards $=52-16=36$
(i) Probability $=\dfrac{3}{36}=\dfrac{1}{12}$
(ii) Probability $=\dfrac{24}{36}=\dfrac{2}{3}$
Question 6 of 30

6. Question
1 point(s)
A bag contains cards numbered 3 to 102, one card is drawn at random. Find the probability that it is :
(a) an even number
(b) a number divisible by 5
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Hint

Total cards $=(102-3)+1=100$
(a) No. of even number $=\dfrac{(102-3)+1}{2}$
$=\dfrac{100}{2}=50$
P(an even no.) $=\dfrac{50}{100}=\dfrac{1}{2}$
(b) Number of numbers divisible by
$5=\dfrac{(102-3)+1}{5}=\dfrac{100}{5}=20$
P(no. divisible by 5) $=\dfrac{20}{100}=\dfrac{1}{5}$
Question 7 of 30

7. Question
1 point(s)
Two dice are thrown together. Determine the probability of 2 coming on the first die and multiple of 3 on other die.
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Hint

Favourable events could be (2, 3) and (2, 6)
Probability $=\dfrac{2}{36}=\dfrac{1}{18}$
Question 8 of 30

8. Question
1 point(s)
Geeta and Sita are friends. What is the probability that both will have
(a) different birthdays ?
(b) the same birthday ?
(ignoring a leap year)
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Hint

(i) $P=\dfrac{365\times364}{365\times365}=\dfrac{364}{365}$
(ii) P(same birthday) $=\dfrac{1}{365}$
Question 9 of 30

9. Question
1 point(s)
A bag contains 5 black, 7 red and 3 white balls. A ball is drawn from the bag at random. Find the probability that the ball drawn is :
(a) black or white
(b) not black
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Hint

Total balls $=5+7+3=15$
(a) P(black or white) $=\dfrac{8}{15}$
(b) P(not black) $=\dfrac{10}{15}=\dfrac{2}{3}$
Question 10 of 30

10. Question
1 point(s)
Cards marked with numbers 3, 4, 5, ……, 50 are placed in a box and mixed thoroughly. One card is drawn at random from the box. Find the probability that the number on the drawn card is
(a) divisible by 7.
(b) is a perfect square.
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Hint

Total no. of cards $=50-2=48$
(i) Numbers divisible by $7=7$
P(getting a number divisible by 7) $=\dfrac{7}{48}$
(ii) Perfect square numbers $=4,9,16,25,36,49$
$P=\dfrac{6}{48}=\dfrac{1}{8}$
Question 11 of 30

11. Question
1 point(s)
Cards, marked with numbers 5 to 50, are placed in a box and mixed thoroughly. A card is drawn from the box at random. Find the probability that the number on the taken card is :
(a) a prime number less than 10
(b) a number which is a perfact square.
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Hint

Total cards = 46
(i) Prime numbers less than 10 = 5 and 7
P(prime no.) $=\dfrac{2}{46}=\dfrac{1}{23}$
(ii) No. of perfect squares = 5
$P=\dfrac{5}{46}$
Question 12 of 30

12. Question
1 point(s)
Two dice are thrown simultaneously. Find the probability that the sum of the two numbers appearing on the top is less than or equal to 10.
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Hint

Total outcomes = 36
$P(sum\le10)=1-\left(\dfrac{2}{36}+\dfrac{1}{36}\right)\\ \\ =1-\dfrac{3}{36}=\dfrac{11}{12}$
Question 13 of 30

13. Question
1 point(s)
A die is thrown once. What is the probability of getting a number greater than 4?
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Hint

Total number greater than
$4=2\\ \\ P=\dfrac{2}{6}=\dfrac{1}{3}$
Question 14 of 30

14. Question
1 point(s)
Two dice are thrown simultaneously. What is the probability that the sum of the numbers appearing on the dice is:
(a) 7?
(b) a prime number?
(c) 1?
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Hint

(i) Sum as $7=6$
$P=\dfrac{6}{36}=\dfrac{1}{6}$
(ii) $n(E)=15$
$P(E)=\dfrac{15}{36}=\dfrac{5}{12}$
(iii) P(sum 10) $=\dfrac{3}{36}=\dfrac{1}{12}$
Question 15 of 30

15. Question
1 point(s)
A bag contains 5 red balls, 8 white balls, 4 green balls and 7 black balls. If one ball is drawn at random, find the probability that it is :
(a) black
(b) red
(c) not green
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Hint

Total balls $=5+8+4+7=24$
(i) P(black) $=\dfrac{7}{24}$
(ii) P(red) $=\dfrac{5}{24}$
(iii) P(not green) $=\dfrac{20}{24}=\dfrac{10}{12}=\dfrac{5}{6}$
Question 16 of 30

16. Question
1 point(s)
A dice has it is six faces marked 0, 1, 1, 1, 6, 6,. Two such dice are thrown together and the total score is recorded.
(a) How many different score-s are available?
(b) What is the probability of getting a total of 7?
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Hint

Total sample space $=6^2=36$
(i) Number of favourable outcomes are (0, 0), (0, 1), (0, 6), (1, 0), (1, 1), (1, 6), (6, 0), (6, 1), (6, 6)
Different score which are possible are 6 scores i.e. 0, 1, 2, 6, 7, 12
(ii) $n(E)=12\\ \\ P(E)=\dfrac{12}{36}=\dfrac{1}{3}$
Question 17 of 30

17. Question
1 point(s)
What is the probability that a number selected at random from the numbers 1, 2, 2, 3, 3, 3, 4, 4, 4, 4 will be their average?
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Hint

average $=\dfrac{30}{10}=3$
Number of favourable outcomes $=3$
$P=\dfrac{3}{10}$
Question 18 of 30

18. Question
1 point(s)
In the figure, each circle touch other two circles externally. The circles are congruent. If a point is selected at random from the interior of square PQRS, find the probability that it will not be in the shaded region.
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Hint

Area of shaded region
$=(2r)^2-4\times\dfrac{\pi r^2}{4}\\ \\ =4r^2-\pi r^2=A$
P(not on shaded region)
$=1-\dfrac{4r^2-\pi r^2}{4r^2}\\ \\ =1-\dfrac{4-\pi}{4}=\dfrac{4-4+\pi}{4}=\dfrac{\pi}{4}$
Question 19 of 30

19. Question
1 point(s)
A child’s game has 8 triangles, of which 3 are blue and rest are red, and 10 squares of which 6 are blue ad rest are red. One piece is lost at random. Find the probability that it is a :
(a) triangle
(b) square
(c) square of blue colour
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Hint

(i) P(lost piece is triangle) $=\dfrac{8}{18}=\dfrac{4}{9}$
(ii) P(lost piece is square) $=\dfrac{10}{18}=\dfrac{5}{4}$
(iii) P(square of blue colour) $=\dfrac{6}{18}=\dfrac{1}{3}$
Question 20 of 30

20. Question
1 point(s)
The number of matchsticks in 10 boxes is an follows : 48, 46, 46, 45, 48, 47, 46, 44, 49, 45 one box is selected at random. Find the probability of the box contaning :
(a) 49 matchsticks
(b) 46 matchsticks
(c) more than 47 matchsticks
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Hint

Total matchsticks = 10
(i) P(49 matchsticks) $=\dfrac{1}{10}$
(ii) P(46 matchsticks) $=\dfrac{3}{10}$
(iii) P(more than 47 matchsticks) $=\dfrac{2}{16}=\dfrac{1}{5}$
Question 21 of 30

21. Question
1 point(s)
A box contains 5 red balls, 3 yellow balls, 3 white balls and 2 black balls. A ball is drawn from the box. Find the probability that it is:
(a) a white ball
(b) a yellow or a black ball
(c) a ball which is not red.
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Hint

Total balls $=5+3+3+2=13$
(i) P(a white ball) $=\dfrac{3}{13}$
(ii) P(yellow or black) $=\dfrac{5}{13}$
(iii) P(ball which is not red) $=\dfrac{8}{13}$
Question 22 of 30

22. Question
1 point(s)
A bag contains 24 balls of which x are red, 2x are white are 3x are blue. A ball is selected at random. What is the probability that it is :
(a) not red?
(b) white?
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Hint

Total balls = 24
$\Rightarrow x+2x+3x=24\Rightarrow x=4$
Red balls = 4, white balls $=2\times4=8$ balls
blue balls $=3\times 4=12$
(i) P(not red) $=\dfrac{20}{24}=\dfrac{5}{6}$
(ii) P(white) $=\dfrac{8}{24}=\dfrac{1}{3}$
Question 23 of 30

23. Question
1 point(s)
In my house the geyser is kept on 24 hours a day. Because of the thermostat setting, it automatically turns off for a total of $4\dfrac{1}{2} $ hours a day. A red light is shown when the power is on. What is the probability that the light will be
(a) off
(b) on if it is looked at random
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Hint

Total time day = 24
(i) $P(E)=\dfrac{4.5}{24}=\dfrac{45}{240}=\dfrac{3}{16}$
(ii) $1-P(E)=1-\dfrac{3}{16}=\dfrac{13}{16}$
Question 24 of 30

24. Question
1 point(s)
Suppose you drop a die at random on the rectangular region shown in figure. What is the probability that it will land inside the circle with diameter 1 m?
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Hint

Area of circle $=\pi r^2=\pi\left(\dfrac{1}{2}\right)^2=\dfrac{\pi }{4}$
Area of rectangle $=3\times2=6$
P(Die will land in the circle)
$=\dfrac{\dfrac{\pi}{4}}{6}=\dfrac{\pi }{24}$
Question 25 of 30

25. Question
1 point(s)
A lot consists of 48 mobile phones of which 42 are good, 3 have only minor defects and 3 have major defects. Saroj will buy a phone if it is good but the trader will buy a mobile if it has no major defect. One phone is seleted at random from the lot. What is the probability that it is
(a) acceptable to Saroj?
(b) acceptable to the trader?
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Hint

(i) $n(E)=42\\ \\ n(S)=48\\ \\ P(E)=\dfrac{42}{48}=\dfrac{7}{8}$
(ii) $n(E)=45\\ \\ P(E)=\dfrac{45}{48}=\dfrac{15}{16}$
Question 26 of 30

26. Question
1 point(s)
A die is thrown twice. What is the probability that“
(a) 5 will not come up either time?
(b) 5 will come up at least once?
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Hint

(i) P(5 will not come up either time) $=\dfrac{25}{36}$
(ii) P(5 will come up at least once) $=\dfrac{11}{36}$
Question 27 of 30

27. Question
1 point(s)
In a single throw of two dice, find the probability of getting
(a) a total of 11
(b) doublets
(c) 6 as a product
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Hint

(i) P(total of 11) $=\dfrac{2}{36}=\dfrac{1}{18}$
(ii) $n(E)=6\\ \\ P(E)=\dfrac{6}{36}=\dfrac{1}{6}$
(iii) P(6 as a product) $=\dfrac{4}{36}=\dfrac{1}{9}$
Question 28 of 30

28. Question
1 point(s)
Two dice are numbered 1, 2, 3, 4, 5, 6 and 1, 1, 2, 2, 3, 3 respectively. They are thrown and the sum of the numbers on them is noted. Find the probability getting each sum from 2 to 9 separately.
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Hint

Sum of $2=\dfrac{2}{36}=\dfrac{1}{18}$
Sum of $3=\dfrac{4}{36}=\dfrac{1}{9}$
sum of $4=\dfrac{4}{36}=\dfrac{1}{9}$
sum of $5=\dfrac{6}{36}=\dfrac{1}{6}$
sum of $6=\dfrac{6}{36}=\dfrac{1}{6}$
sum of $7=\dfrac{6}{36}=\dfrac{1}{6}$
sum of $8=\dfrac{4}{36}=\dfrac{1}{9}$
sum of $9=\dfrac{2}{36}=\dfrac{1}{18}$
Question 29 of 30

29. Question
1 point(s)
Three coins are tossed simultaneously. Find the probability of getting.
(a) three heads
(b) exactly 2 heads
(c) at least 2 heads
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Hint

$(HHH),(HHT),(HTH),(THH),(TTT),(TTH),(THT),(HTT)$
(a) P(three heads) $=\dfrac{1}{8}$
(b) P(exactly two heads) $=\dfrac{3}{8}$
(iii) P(at least 2 heads) $=\dfrac{4}{8}=\dfrac{1}{2}$
Question 30 of 30

30. Question
1 point(s)
A box contains 17 cards numbered 1, 2, 3, …….. 16, 17. A card is drawn at random from the box. Find the probability that the number on the drawn card is :
(a) odd
(b) even and prime
(c) divisible by 3
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Hint

(i) $P(E)=\dfrac{9}{17}$
(ii) P(even and prime) $=\dfrac{1}{17}$
(iii) P(number divisible by 3) $=\dfrac{5}{17}$

Maths Class X Question Bank

Questions Bank-Essay Type 2-Probability – Class X

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