CBSE Important Mathematics Questions of Class X Chapter {Probability} for CBSE Examination 2023
1)
Find the sum of probability of all
the events of the experiment.
2)
What is the probability of sure event?
3)
Two dice are thrown simultaneously.
Find the probability of getting a prime number on both dice.
4)
Find the probability of getting a
perfect square number from the numbers 1 to 10.
5)
Two coins are tossed together. Find
the probability of getting head on both.
6)
Two dice are thrown together. Find
the probability of getting the same number on both dice.
7)
If a die is thrown once, find the
probability of getting a number less than 3 and greater than 2.
8)
Two different dice are tossed
together. Find the probability that the product of two numbers on the top of
the dice is 6.
9)
In a throw of two coins, find the
probability of getting a sum of 10.
10) From a pack of 52 playing cards, a card is drawn at random. Find
the probability that the drawn card is not a face card.
11) A die is thrown once. Find the probability of getting an even
number less than 5.
12) In a simultaneous toss of two coins, find the probability of
exactly one head.
13) A game of chance consists of spinning and arrow which comes to
rest Pointing add one of the numbers 1, 2, 3, 4, 5, 6, 7, 8 and these are
equally likely outcomes. Find the probability that the arrow will point at any
factor of 8.
14) The probability of getting a Rotten egg from a lot of 400 eggs is
0.035. Find the number of rotten eggs in the lot.
15) A box contains cards numbered 6 to 50. a card is drawn at random
from the box. Find the probability that the drawn card has a number which is a
perfect square.
16) The probability of guessing the correct answer to certain question
is p/12. If the probability of not getting the correct answer to same question
is ¾ then find the value of p.
17) A letter of English alphabet is chosen at random. Determine the
probability that the letter is a consonant.
18) Find the probability of getting multiple of 3 in a single throw of
an ordinary die.
19) Cards marked with number 3, 4, 5……. 50 are placed in a box and
mixed thoroughly. A card is drawn at random from the box. Find the probability
that the selected card bears a perfect square number.
20) A coin is tossed 2 times. Find the probability of getting at most
one head.
21) A single letter is selected at random from the word probability. Find
the probability that is a vowel.
22) If the probability of an event p, then what will be the
probability of its complementary event?
23) 20 tickets on which numbers 1 to 20 are written, are mixed
thoroughly and then a ticket is drawn at random out of them. Find the City that
the number on the drawn ticket is a multiple of 7 or 3.
24) A card is drawn at random from a well shuffled pack of 52 playing
cards. Find the probability of getting neither a red card nor a queen.
25) 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.
26) A card is drawn at random from a well shuffled pack of 52 playing
cards. Find the probability of getting a red king and a black queen.
27) Two dice are thrown simultaneously. Find the probability that the
sum of the two numbers appearing on their tops is less than or equal to 10.
28) Two dice are thrown together. Determine the probability of 2
coming on the first dice and multiple of 3 on other dice.
29) A bag contains 2 green, 3 red and 4 Black balls. A ball is taken
out of the bag at random. Find the probability that the selected ball is not
black and not Green.
30) From a well shuffled pack of cards, a card is drawn at random. Find
the probability of getting a black queen.
31) Two coins are tossed simultaneously. Find the probability of
getting at least one head.
32) From a group of 2 boys and 2 girls, two children are selected at
random. What is the sample space representing the event. Find the probability
that one boy and one girl is selected.
33) 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 black or
white and not black.
34) A game of chance consists of spinning and arrow which comes to
rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8 and these are
equally likely outcomes. what is the probability that it will point at:
a)
a prime number
b)
a factor of 8
35) A jar contains 24 marbles, some are green and other are blue. If a
marble is drawn at random from the jar, the probability that it is green is ⅔
.find the number of blue marbles.
36) Apoorv throws two dice once it completes the product of the
numbers appearing on the dice. Renu throws one die and squares the number
that appears on it. Who has the better chance of getting the number 36?
37) A bag contains 14 balls of which X are white. If 6 more white
balls are added to the bag, the probability of drawing a white ball is 1/2.
Find the value of x.
38) Two friends were born in the year 2000. What is the probability
that they have the same birthday?
39) A number is selected at random from first 50 natural numbers. Find
the probability that it is a multiple of 3 and 4.
40) What is the probability that a non leap year selected randomly
will have 53 Sundays?
41) Two dice are thrown at the same time. find the probability of
getting
a)
same number on both dice
b)
different number on both dice
42) Three different coins are tossed together find the probability of
getting
a)
exactly two heads
b)
at least two heads
c)
at least 2 tails
43) From a pack of 52 playing cards, Jacks, Queens and Kings of red
colour are removed. from the remaining a card is drawn at random. find the
probability that drawn card is:
a)
a black king
b)
a card of red colour
c)
a card of black colour
44) There are 100 cards in a bag on which number 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
a)
is divisible by 9 and is a perfect
square
b)
is a prime number greater than 80.
45) In a single throw of a pair of different dice, what is the
probability of getting
a)
a prime number on each dice?
b)
a total of 9 or 11?
46) Two different dice are thrown together find the probability of:
a)
getting a number greater than 3 on
each dice
b)
getting a total of 6 or 7 of the
numbers on two dice.
47) A bag contains 18 balls out of which X balls are red
a)
If one ball is drawn at random from
the bag, what is the probability that it is not red?
b)
If two more red balls are put in
the bag, the probability of drawing a red ball will be 9/8 times the probability
of drawing a red ball in the first case. Find the value of x.
48) The probability of selecting
are red ball at random from a jar that contains only red, blue and orange balls
is ¼. The probability of selecting a blue ball at random from the same jar is
⅓. If the jar contains 10 Orange balls, find the total number of balls in the
jar.
49) Two different dice are
rolled together. find the probability of getting
a) the sum of numbers on two Dice to be 5
b) Even Numbers on both dice
50) Two dice are thrown simultaneously. what is the probability that the sum of the numbers appearing on the dice is
a) 7
b) not a prime number?
c) 1
51) In a game the entry fees is Rs 5. the game consists of tossing a coin 3 times. if one or two heads show Shweta gets her entry fees back. if she tosses 3 heads she receive double the entry fees. otherwise she will lose. for tossing a coin 3 times, find the probability that she
a) losses the entry fees.
b) get double entry fees
c) just gets her entry fees
52) A game of chance consists of an arrow which comes to rest Pointing at one of the reasons 1, 2 or 3. O is the centre of the circle. find the probability that
a) arrow is resting on 3
b) Arrow is resting on 1.
c) Arrow is not resting on 2.
53) One card is drawn from a well shuffled Deck of 52 cards. calculate the probability that the card will:
a) Be an ace
b) Not be an ace.
54) A box contains card numbered 3, 5, 7, 9……, 35, 37. A card is drawn at random from the box. find the probability that the number on the drawn card is a prime number.
55) A card is drawn from a well shuffled Deck of 52 cards. find the probability of getting
a) a king of red colour
b) a face card
c) The queen of Diamonds.
56) A box contains 100 Red cards, 200 yellow cards and 50 blue cards. if a card is drawn at random from the box, then find the probability that it will be:
a) a blue card
b) not a yellow card
c) neither yellow nor a blue card.
57) A box contains 35 blue, 25 white and 40 red marbles. if a marble is drawn at random from the box, find the probability that the drawn marble is:
a) White
b) not blue
c) neither white nor blue
58) A box contains 70 cards numbered from 1 to 70. if one card is drawn at random from the box, find the probability that it bears:
a) a perfect square number
b) a number divisible by 2 and 3
59) Ankita and Nagma are two friends. They were both born in 1990. what is the probability that they have
a) same birthday
b) different birthday?
a) A piggy bank contains hundred 50 paise coins, fifty Rs 1 coins, twenty Rs2 coins and ten Rs 5 coins .if it is equally likely that one of the coins will fall out when then bank is turned upside down, then what is the probability that the coin
a. will be of 50 paise coin?
b. will not be a 5 rupee coin?
60) A die is thrown once. find the probability of getting
a) a prime number
b) a number lying between 2 and 6
c) an odd number
61) 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 a good, but will not by if it is defective. The shopkeeper draws one pen at random and gives it to her. What is the probability that
a) she will buy it?
b) she will not buy it?
62) A number X is selected at random from the numbers 1, 4, 9, 16 and another number Y is selected at the random from the numbers 1, 2, 3, 4. Find the probability that the value of xy is more than 16.
63) A box contains card bearing numbers from 6 to 70. if one card is drawn at random from the box, find the probability that it bears:
a) a one digit number
b) a number divisible by 5
c) an odd number less than 30
d) a composite number between 50 and 70
64) A card is drawn at random from a well shuffled Deck of playing cards. find the probability that the card drawn is
a) a card of spade or an Ace
b) a black king
c) neither a Jack Noah king
d) either the king or a queen
65) A box contains 20 cards numbered from 1 to 20. a card is drawn at random from the box .find the probability that the number on the drawn card is
a) divisible by 2 or 3
b) a prime number
66) A box contains 12 balls out of which X are black. If one ball is drawn at random from the box, what is the probability that it will be a black ball? If 6 more black balls are put in the box, the probability of drawing a black ball now is double of what it was before. Find x.
67) Cards numbered 1 to 30 are put in a bag. A card is drawn at random from this bag. Find the probability that the number on the drawn card is
a) not divisible by 3
b) a prime number greater than 7
68) All the black face cards are removed from a pack of 52 playing cards. the remaining cards are well shuffled and then a card is drawn at random, find the probability of getting a
a) face card
b) red card
c) black card
d) King
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