ICSE Class 10

General instructions: Answer all questions. Marks are shown in brackets [ ].

Objective

1. 1.
   A card is drawn from a pack of 100 cards numbered 1 to 100. What is the probability of drawing a number which is a perfect square?

   1. A. 1/5
   2. B. 1/10
   3. C. 1/20
   4. D. 1/100
   [1]
2. 2.
   A game consists of tossing a one-rupee coin 3 times and noting the outcome each time. Ramesh wins if all tosses show the same result (all heads or all tails) and loses otherwise. What is the probability that Ramesh will lose the game?

   1. A. 1/4
   2. B. 1/2
   3. C. 3/4
   4. D. 7/8
   [1]
3. 3.
   A bag contains 5 white, 2 red, and 3 black balls. A ball is drawn at random. What is the probability that the ball drawn is a red ball?

   1. A. $\frac{1}{10}$
   2. B. $\frac{1}{5}$
   3. C. $\frac{3}{10}$
   4. D. $\frac{2}{5}$
   [1]
4. 4.
   Two different dice are thrown together. What is the probability that the sum of the numbers appeared is less than 5?

   1. A. 1/12
   2. B. 1/6
   3. C. 1/4
   4. D. 1/3
   [1]
5. 5.
   The probability that two boys do not have the same birthday is 0.897. What is the probability that the two boys have the same birthday?

   1. A. 0.103
   2. B. 0.897
   3. C. 0.013
   4. D. 1.897
   [1]
6. 6.
   Two coins are tossed simultaneously 125 times and it was observed that both heads appeared 15 times. If two coins are tossed simultaneously at random, what is the probability of getting both heads?

   1. A. 15/125
   2. B. 3/25
   3. C. 1/4
   4. D. 15/100
   [1]
7. 7.
   A number is chosen at random from the numbers $-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5$. Then the probability that the square of this number is less than or equal to 1 is:

   1. A. $\frac{8}{11}$
   2. B. $\frac{3}{11}$
   3. C. $\frac{6}{11}$
   4. D. $\frac{7}{11}$
   [1]
8. 8.
   If a card is selected from a deck of 52 cards, then what is the probability of its being a red face card?

   1. A. $\frac{23}{26}$
   2. B. $\frac{3}{26}$
   3. C. $\frac{6}{13}$
   4. D. $\frac{7}{13}$
   [1]
9. 9.
   A bag contains 15 white and some black balls. If the probability of drawing a black ball from the bag is thrice that of drawing a white ball, what is the number of black balls in the bag?

   1. A. 15
   2. B. 30
   3. C. 45
   4. D. 60
   [1]
10. 10.
    A book contains 85 pages. A page is chosen at random. What is the probability that the sum of the digits on the page is 8?

    1. A. 8/85
    2. B. 9/85
    3. C. 10/85
    4. D. 7/85
    [1]
11. 11.
    Someone is asked to take a number from 1 to 100. What is the probability that it is a prime?

    1. A. 1/5
    2. B. 1/4
    3. C. 3/4
    4. D. 2/5
    [1]
12. 12.
    Someone is asked to take a number from 1 to 100. The probability that it is a prime is:

    1. A. $\frac{8}{25}$
    2. B. $\frac{1}{4}$
    3. C. $\frac{3}{4}$
    4. D. $\frac{13}{50}$
    [1]
13. 13.
    Two dice are thrown together. The probability that the sum of the two numbers will be a multiple of 4 is:

    1. A. $\frac{1}{2}$
    2. B. $\frac{1}{3}$
    3. C. $\frac{1}{8}$
    4. D. $\frac{1}{4}$
    [1]
14. 14.
    A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball is three times that of a red ball, how many blue balls are in the bag?

    1. A. 5 blue balls
    2. B. 10 blue balls
    3. C. 15 blue balls
    4. D. 20 blue balls
    [1]
15. 15.
    Peter throws two different dice together and finds the product of the two numbers obtained. Rina throws a die and squares the number obtained. Who has a better chance to get the number 25?

    1. A. Peter has a better chance.
    2. B. Rina has a better chance.
    3. C. Both have an equal chance.
    4. D. Neither can get the number 25.
    [1]
16. 16.
    The probability of selecting a blue marble at random from a jar that contains only blue, black, and green marbles is 1/5. The probability of selecting a black marble at random from the same jar is 1/4. If the jar contains 11 green marbles, what is the total number of marbles in the jar?

    1. A. 22 marbles
    2. B. 44 marbles
    3. C. 55 marbles
    4. D. 66 marbles
    [1]
17. 17.
    A letter is chosen at random from the letters of the word ASSASSINATION, then the probability that the letter chosen is a vowel in the form of $\frac{6}{2x + 1}$, then $x$ is equal to:

    1. A. 5
    2. B. 6
    3. C. 7
    4. D. 8
    [1]
18. 18.
    Which of the following relationship is the correct?

    1. A. $P(E) + P(\overline{E}) = 1$
    2. B. $P(\overline{E}) - P(E) = 1$
    3. C. $P(E) = 1 + P(\overline{E})$
    4. D. None of these
    [1]
19. 19.
    A bag contains 20 balls out of which $x$ are red. If one ball is drawn at random, what is the probability that it is not red? It is given that when 5 more red balls are added, the probability of drawing a red ball doubles compared to before. Find the value of $x$.

    1. A. $x = 3$
    2. B. $x = 5$
    3. C. $x = 7$
    4. D. $x = 10$
    [1]
20. 20.
    A pair of dice is thrown. What is the probability of getting a sum of 10 or more, given that 5 appears on the first die?

    1. A. 1/6
    2. B. 1/18
    3. C. 1/12
    4. D. 1/3
    [1]