Vardaan Learning Institute

Chapter Practice Sheet: Probability

Class: 10 (CBSE) Subject: Mathematics Max. Marks: 50
SECTION A: OBJECTIVE TYPE QUESTIONS (1 Mark Each)
1. The probability of an impossible event is:
  1. 1
  2. 0
  3. Less than 0
  4. Greater than 1
[1]
2. If $P(E) = 0.05$, then the probability of 'not E' is:
  1. 0.5
  2. 0.95
  3. 0.05
  4. 0.9
[1]
3. A card is drawn from a well-shuffled deck of 52 cards. The probability that it is a face card is:
  1. 12/52
  2. 3/13
  3. 4/13
  4. 1/13
[1]
4. Which of the following cannot be the probability of an event?
  1. 2/3
  2. -1.5
  3. 15%
  4. 0.7
[1]
5. The probability of getting a prime number in a single throw of a die is:
  1. 1/2
  2. 1/3
  3. 1/6
  4. 2/3
[1]
6. Two coins are tossed strictly. The probability of getting at most one head is:
  1. 1/4
  2. 1/2
  3. 3/4
  4. 1
[1]
7. If an event cannot occur, then its probability is:
  1. 1
  2. 3/4
  3. 1/2
  4. 0
[1]
8. The probability of selecting a rotten apple randomly from a heap of 900 apples is 0.18. What is the number of rotten apples in the heap?
  1. 18
  2. 81
  3. 162
  4. 180
[1]
9. The probability of getting a bad egg in a lot of 400 is 0.035. The number of bad eggs in the lot is:
  1. 7
  2. 14
  3. 21
  4. 28
[1]
10. The probability of a non-leap year having 53 Sundays is:
  1. 1/7
  2. 2/7
  3. 5/7
  4. 6/7
[1]
SECTION B: SHORT ANSWER TYPE QUESTIONS (2 Marks Each)
11. A bag contains 3 red balls and 5 black balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is (i) red? (ii) not red?
[2]
12. A die is thrown once. Find the probability of getting (i) a number lying between 2 and 6 (ii) an odd number.
[2]
13. One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting (i) a king of red colour (ii) a spade.
[2]
14. A letter is chosen at random from the word "ASSASSINATION". Find the probability that the letter chosen is a vowel.
[2]
SECTION C: SHORT ANSWER TYPE II QUESTIONS (3 Marks Each)
15. 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.
[3]
16. A piggy bank contains hundred 50p coins, fifty ₹1 coins, twenty ₹2 coins and ten ₹5 coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down, what is the probability that the coin (i) will be a 50p coin? (ii) will not be a ₹5 coin?
[3]
17. Two dice are thrown at the same time. Find the probability that the sum of the two numbers appearing on the top of the dice is (i) 8 (ii) 13 (iii) less than or equal to 12.
[3]
18. Five cards—the ten, jack, queen, king and ace of diamonds, are well-shuffled with their face downwards. One card is then picked up at random.
(i) What is the probability that the card is the queen?
(ii) If the queen is drawn and put aside, what is the probability that the second card picked up is (a) an ace? (b) a queen?
[3]
19. A box contains 3 blue, 2 white and 4 red marbles. If a marble is drawn at random from the box, what is the probability that it will be: (i) white? (ii) blue? (iii) red?
[3]
20. A lot consists of 144 ball pens of which 20 are defective and the others are good. Nuri will buy a pen if it is good, but will not buy if it is defective. The shopkeeper draws one pen at random and gives it to her. What is the probability that: (i) She will buy it? (ii) She will not buy it?
[3]
SECTION D: LONG ANSWER TYPE QUESTIONS (5 Marks Each)
21. A jar contains 24 marbles, some are green and others are blue. If a marble is drawn at random from the jar, the probability that it is green is 2/3. Find the number of blue marbles in the jar. Also find the probability of drawing a blue marble if 4 more green marbles are added to the jar.
[5]
22. All the jacks, queens and kings are removed from a deck of 52 playing cards. The remaining cards are well shuffled and then one card is drawn at random. Giving ace a value 1, similar value for other cards, find the probability that the card has: (i) The value 7 (ii) The value greater than 7 (iii) The value less than 7 (iv) A prime number value (v) A face card value
[5]
SECTION E: CASE STUDY (4 Marks)
23. Case Study: The Game of Choice
In a family game night, Rahul proposes a game involving two spinners. Spinner A has numbers 1, 2, 3 and Spinner B has colors Red, Blue, Green, Yellow. The result of a turn is determined by spinning both.

(i) Write the sample space of all possible outcomes. (1 Mark)
(ii) What is the probability of getting an even number and the color Red? (1 Mark)
(iii) What is the probability of getting a number less than 3 and any color except Yellow? (1 Mark)
(iv) If the game is won by getting an odd number and a primary color (Red, Blue, Yellow), what is the probability of winning? (1 Mark)
[4]