CBSE Class 10 Mathematics Probability And Constructions Worksheet Set A

Question. Two dice are thrown at a time, then find the probability that the difference of the numbers shown on the dice is 1.
(a) 3/16
(b) 5/18
(c) 7/36
(d) 7/18

Answer: B

Question. A book containing 100 pages is opened at random. Find the probability that a doublet page is found.
(a) 8/25
(b) 9/100
(c) 7/100
(d) 11/100

Answer: B

Question. When two dice are thrown, find the probability of getting a number always greater than 4 on the second dice.
(a) 2/3
(b) 1/3
(c) 3/5
(d) 2/5

Answer: B

Question. Two numbers are chosen from 1 to 5. Find the probability for the two numbers to be consecutive.
(a) 3/5
(b) 2/5
(c) 4/5
(d) 2/3

Answer: B

Question. An unbiased die is rolled twice. Find the probability of getting the sum of two numbers as a prime
(a) 3/5
(b) 5/12
(c) 7/12
(d) 4/5

Answer: B

Question. Two fair dice are thrown. Find the probability that both dice show different numbers.
(a) 1/6
(b) 5/6
(c) 32/36
(d) 29/36

Answer: B

Question. A bag contains 40 coins, consisting of ₹2,₹5 and `10 denominations. If a coin is drawn at random, the probability of drawing a ₹2 coin is 5/8. If x number of ₹2 coins are removed from the bag and then a coin is drawn at random, the probability of drawing a ₹2 coin is 1/2. Find the value of x.
(a) 5
(b) 2
(c) 10
(d) 8

Answer: C

Question. A factory has 120 workers in January, 90 of them are female workers. In February, another 15 male workers were employed. A worker is then picked at random. Calculate the probability of picking a female worker.
(a) 3/4
(b) 4/9
(c) 2/3
(d) 1/2

Answer: C

Question. A box contains a number of marbles with serial number 18 to 38. A marble is picked at a random. Find the probability that it is a multiple of 3.
(a) 3/5
(b) 7/20
(c) 3/4
(d) 1/3

Answer: D

Question. One card is drawn from a well shuffled deck of 52 cards.
I. The probability that the card will be diamond, is 1/2.
II. The probability of an ace of heart is 1/52.
III. The probability of not a heart is 3/4.
IV. The probability of king or queen is 1/26.
Which of the statement(s) is/are true?
(a) I and II
(b) II and III
(c) III and IV
(d) none of the options

Answer: B

Question. A fair die is thrown once. The probability of getting a composite number less than 5 is
(a) 1/3
(b) 1/6
(c) 2/3
(d) 0

Answer: B

Question. If a letter is chosen at random from the letter of English alphabet, then the probability that it is a letter of the word ‘DELHI’ is
(a) 1/5
(b) 1/26
(c) 5/26
(d) 21/26

Answer: C

Question. The probability of raining on day 1 is 0.2 and on day 2 is 0.3. The probability of raining on both the days is
(a) 0.2
(b) 0.1
(c) 0.06
(d) 0.25

Answer: C

Question. Which of the following cannot be the probability of an event?
(a) 2/3
(b) – 1/5
(c) 15%
(d) 0.7

Answer: B

Question. The probability that a two digit number selected at random will be a multiple of ‘3’ and not a multiple of ‘5’ is
(a) 2/15
(b) 4/15
(c) 1/15
(d) 4/90

Answer: B

Question. The probability of getting a number greater than 2 in throwing a die is
(a) 2/3
(b) 1/3
(c) 4/3
(d) 1/4

Answer: A

Question. Out of one digit prime numbers, one number is selected at random. The probability of selecting an even number is
(a) 1/2
(b) 1/4
(c) 4/9
(d) 2/5

Answer: B

Question. A single letter is selected at random from the word “PROBABILITY”. The probability that the selected letter is a vowel is
(a) 2/11
(b) 3/11
(c) 4/11
(d) 0

Answer: C

Question. A three digit number is to be formed using the digits 3, 4, 7, 8 and 2 without repetition. The probability that it is an odd number is
(a) 2/5
(b) 1/5
(c) 4/5
(d) 3/5

Answer: A

Question. An urn contains 6 blue and ‘a’ green balls. If the probability of drawing a green ball is double that of drawing a blue ball, then ‘a’ is equal to
(a) 6
(b) 18
(c) 24
(d) 12

Answer: D

Question. Two coins are tossed simultaneously. The probability of getting at most one head is
(a) 1/4
(b) 1/2
(c) 3/4
(d) 1

Answer: C

Question. If in a lottery, there are 5 prizes and 20 blanks, then the probability of getting a prize is
(a) 2/5
(b) 4/5
(c) 1/5
(d) 1

Answer: C

Question. Which of the following relationship is the correct ?
(a) P (E) + P (E) = 1
(b) P (E) – P(E) = 1
(c) P(E) = 1 + P (E)
(d) none of the options

Answer: A

Question. For an event E, P (E) + P(E) = q, then
(a) 0  q < 1
(b) 0 < q  1
(c) 0 < q < 1
(d) none of the options

Answer: D

Question. A girl calculates that the probability of her winning the first prize in a lottery is 0.08. If 6000 tickets are sold, how many tickets has she bought?
(a) 40
(b) 240
(c) 480
(d) 750

Answer: C

Question. Three - digit numbers formed by using digits 0, 1, 2 and 5 (without repetition) are written on different slips with distinct number on each slip, and put in a bowl. One slip is drawn at random from the bowl. The probability that the slip bears a number divisible by 5 is
(a) 5/9
(b) 4/9
(c) 2/3
(d) 1/3

Answer: A

Question. A box contains four cards numbered as 1, 2, 3 and 4 and another box contains four cards numbered as 1, 4, 9 and 16. One card is drawn at random from each box. What is the probability of getting the product of the two numbers so obtained , more than 16?
(a) 5/8
(b) 1/2
(c) 3/8
(d) 1/4

Answer: C

Question. From the data (1, 4, 7, 16, 27, 29) if 29 is removed, the probability of getting a prime number is
(a) 1/2
(b) 1/5
(c) 2/5
(d) 1/3

Answer: B

Question. A bag contains card numbers 3, 4, 5, 6, 7....27. One card is drawn, then probability of prime number card is
(a) 9/25
(b) 8/27
(c) 8/25
(d) 1/5

Answer: C

Question. Two dice are rolled, then probability of getting a total of 9 is
(a) 1/3
(b) 1/9
(c) 9/10
(d) 8/9

Answer: B

Question. From a bag containing 100 tickets numbered 1, 2, 3, ........., 100 one ticket is drawn. If the number on this ticket is x,  then the probability that x + 1/+ 1 > 2 is ......
(a) 0
(b) 0.99
(c) 1
(d) none of the options

Answer: B

Question. A coin is tossed. Then the probability of getting either head r tail is
(a) 1
(b) 1/3
(c) 1/2
(d) 1/4

Answer: B

Question. Two dice are rolled simultaneously. Find the probability that they show different faces.
(a) 3/4
(b) 1/6
(c) 1/3
(d) 5/6

Answer: A

Question. A die is thrown once then,
(a) the probability of getting an odd number is 23
(b) the probability of getting multiple of 3 is 1/3
(c) the probability of getting a prime number is 2/3
(d) the probability of getting number greater than 5 is 1/3

Answer: B

Question. The probability of an event can not be
(a) positive
(b) negative
(c) zero
(d) one

Answer: B

Question. If the probability of an event is 0, then it is called a
(a) sure event
(b) certain event
(c) impossible event
(d) none of the options

Answer: C

Question. Which of the following statement(s) is/are not correct ?
(a) An event which can never happen is called impossible event.
(b) An event which has more than one (favourable) outcomes is called a compound event.
(c) The collection of all possible outcomes of an experiment is called sample space.
(d) none of the options

Answer: D

Question. A bag contains 24 balls of which x are red 2x are white and 3x are blue. A ball is selected at random. What is the probability that
(i) it is red
(ii) it is blue
(iii) neither red nor blue
Answer : 1/6 , 1/2, 2/3

Question. 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?
Answer : 1/5, 1/4, 0

Question. A child’s game has 6 triangles of which 3 are blue and rest are red and 10 squares of which 6 are blue and rest are red. One piece Is lost at random. Find the probability that that it is a
(i) Triangle
(ii) Square
(iii) Square of blue colour
Answer : 3/8, 5/8, 3/8

Question. Out of the families having three children, a family is chosen random. Find the probability that the family has (i) Exactly one girl (ii) At least one girl (iii) At most one girl
Answer : 3/8 , 7/8 , 1/2

Question. A lot consists of 48 mobile phones of which 42 are good, 3 have only minor defects and 3 have major defects. Varnika will buy a phone if it is good but the trader will only buy a mobile if it has no major defect. One phone is selected at random from the lot. What is the probability that it is: (i) acceptable to. Varnika? (ii) acceptable to the trader?
Answer : 7/8, 15/16

Question. Two dice are thrown simultaneously. What is the probability that: (a) 5 will not come up either of them?
(b) 5 will come up on at least one time?
(c) 5 will come at both dice?
(d) Sum of 5 comes on both the dice together
Answer : 25/36 , 11/36 , 1/36 , 1/9

Question. 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: (i) red. (ii) black or white. (iii) not black.
Answer : 7/15, 8/15, 2/3

Question. Cards bearing numbers 3, 5… 35 are kept in a bag. A card is drawn at random from the bag. Find the probability of getting a card bearing (a) a prime number less than 15 (b) a number divisible by 3 and 5
Answer : 5/17, 2/17

Question. 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, find the total number of marbles in the jar.
Answer : 20

Question. There are 100 cards in a bag on which numbers from 1 to 100 are written. A card is taken out from the bag at random. Find the probability that the number on the selected card
I. is divisible by 9 and is a perfect square
II. (ii) is a prime number greater than 80
Answer : 3/100, 3/100

Question. Three coins are tossed simultaneously. Find the probability of getting
(i) Exactly 2 heads (ii) at least 1 head (iii) at most 2 tails (iv) exactly 3 heads
Answer : 3/8, 7/8 , 7/8 , 1/8

Please click on below link to download CBSE Class 10 Mathematics Probability And Constructions Worksheet Set A