15 : Probability
Probability
MOST EXPECTED QUESTIONS AND ANSWERS
15. PROBABILITY
SECTION = A
Q1. If two different dice are rolled together, the probability of getting an even number on both dice is :
(a) 
(b) 
(c) 
(d) 
[2014 Dehli]
Solution : (d)
[ P(getting an even number on both dice) 
]
Q2. Which one of the following is the probability of an event ? [SEBA 2017]
(a) 
(b) 
(c) – 1.5 (d) 1.001
Solution : (a)
[ The probability of an even E is a number P(E) such that 
]
Q3. Two different coins are tossed simultaneously . The probability of getting at least one head is :
(a) (b) 
(c) 
(d) 
[CBSE 2014F]
Solution : (c)
[ P(getting at least one head) 
{ HH , HT , TH } ]
Q4. A bag contain 8 red , 6 white and 4 black balls . A ball is drawn at random from the bag.
Then the probability that the drawn ball getting neither white nor black is :
(a) 
(b) 
(c) 
(d) 
Solution : (b)
[ P(getting neither white nor black) 
]
Q5.The sum of the probabilities of all the elementary events of an experiment is : [SEBA 2020]
(a) 1 (b) 1.25 (c) 1.4 (d) 2
Solution : (a) 1
[ The sum of the probabilities of all the elementary events of an experiment is 1 .]
Q6. The probability that a number selected at random from the numbers 1 , 2 , 3 , ……, 15 is
a multiple of 4 is : [2014]
(a) 
(b) 
(c) 
(d) 
Solution : (d)
[ P(getting a multiple of 4) 
{4 , 8 , 12} ]
Q7. A number is selected from the first 100 natural numbers . The probability that the number
is divisible by 7 is : [SEBA 2016]
(a) 
(b) 
(c) 
(d) 
Solution : (a)
[ P(getting a number divisible by 7) 
{7,14,21,28,35,42,49,56,63,70,77,84,91,98} ]
Q8. If for any event 
, 
, when 
means ‘‘ an event not happen 
’’ then the
value 
is :
(a) 1.00 (b) 9.99 (c) 0.89 (d) 1.11 [SEBA 2014]
Solution: (c) 0.89
[ We have , 
]
Q9. Which of the following cannot be the probability of an event ?
(a) (b) 
(c) 15 % 
(d) 0.7
Solution: (b)
Q10. In a family of 3 children, the probability of having at least one boy is : [ CBSE 2014]
(a) 
(b) 
(c) 
(d) 
Solution : (d)
[ Total number of possible outcome 
The number of at least one boy 
]
Filled in the blanks
Q1. Probability of an event + Probability of the event ‘ not ’ 
.
Solution : 1
[ Since, 
]
Q2. A die is thrown once , then the probability of getting a number greater than 4 is 
.
Solution : 
[ P(getting a number greater than 4) 
{5 , 6} ]
Q3. The probability of an event 
is a number 
such that 
.
Solution : 
.
Q4. One card is drawn from a well-shuffled deck of 52 cards , then the probability of getting
a spade is 
. [SEBA 2018]
Solution : 
[ P(getting a spade) 
]
Q5. The probability that it will rain tomorrow is 0.85 , then the probability that it will not rain
tomorrow is .
Solution : 0.15
[ We have , 
]
Q6. The sum of the probabilities of all the elementary events of an experiment is 
.
Solution: 1
Q7. The probability of an event that is certain to happen is 0 . Such an event
is called 
.
Solution: impossible event .
Q8. For any event , 
, Where 
stands for ‘not 
’. and are called
events .
Solution: Complementary .
Q9. Two players , Sangeeta and Reshma , play a tennis match . It is known that the probability
of Sangeeeta winning the match is 0.62 . Then the probability of Reshma winning the
match is 
.
Solution: 0.38
[ The probability of Reshma’s winning 
]
Q10. The probability of an event is greater than or equal to 
and less than
or equal to 
.
Solution: 0 and 1
Answers following the questions
Q7. A game of chance consists of spinning an 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 . Find the probability that the arrow
will point at any factor of 8 . [2015F]
Solution: The total number of possible outcome 
The number of factor of 8 
Q1. If three different coins are tossed together, then find the probability of getting two heads . [2017C]
Solution : Total number of elementary events 
The favourable number of elementary events 
P(getting two heads) 
Q1. One card is drawn from a well-shuffled deck of 52 cards . Find the probability of getting a spade .
[SEBA 2018]
Solution: Total number of possible outcome 
The number of a spade 
.
Q2. 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 . [2016 Delhi]
Solution : Total number of elementary events 
.
The favourable number of elementary events 
[ 1 , 4 , 9 , 16 , 25 , 36 , 49]
P(getting a perfect square number) 
Q3. Find the probability of getting the letter M in the word ‘‘ MATHEMATICS ’’ .
Solution : Total number of elementary events 
.
The favourable number of elementary events
P(getting the letter M) 
Q4. A letter is chosen at random from the letter of the word ‘‘ PROBABILITY ’’ . Find the probability
that it is not a vowel .
Solution: The total number of word
The number of ‘‘ not a vowel ’’ 
Q5. A bag contains 3 red and 5 black balls . A ball is drawn at random from the bag . What is the
probability that the drawn ball is not red ? [2017C Delhi]
Solution: Total number of balls
Q6. What is the probability of getting a number less than 7 in a single throw of a die ?
Solution: Total number of possible outcome
7. Gopi buys a fish from a shop for his aquarium . The shopkeeper takes out one fish at random
from a tank containing 5 male fish and 8 female fish . What is the probability that the fish taken
out is a male fish ?
Solution: Total number of fishes 
Q4. It is given that a group of 3 students, the probability of 2 students not having the same birthday
is 0.992 . What is the probability that the 2 students have the same birthday .
Solution : 2 students from a groups of 3 students not having the same birthday 
2 students from a group of 3 students having the same birthday 
Q5. 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 . [CBSE 2016]
Solution : Total number of elementary events .
The favourable number of elementary events 
.
P(getting neither a red nor a queen) 
SECTION = B [2 Marks]
Q1. 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 [SEBA 2019]
Solution : Total number of balls = 3 + 5 = 8
(i) P(getting the red balls)
(ii) P(getting not red balls) 
Q2. Two different dice are rolled simultaneously . Find the probability that the sum of numbers
appearing on the two dice is 10 . [2014F]
Solution : Total number of possible outcome = 36
The favourable number of elementary events = 3 [ (4 , 6) , (5 , 5) , (6 , 4) ]
P(getting the sum of numbers appearing on the two dice is 10) 
Q3. A die is thrown once . Find the probability of getting : [SEBA 2017]
(i) a prime number (ii) a number lying between 2 and 6 .
Solution : Total number of possible outcome = 6
(i) The favourable number of elementary events = 3 [ 2 , 3 , 5 ]
P(getting a prime number) 
(ii) The favourable number of elementary events = 3 [3 , 4 , 5 ]
P(getting a number lying between 2 and 6)
Q4. 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 . (iii) a red face card [SEBA 2020]
Solution : Total number of possible outcome = 52
(i) The favourable number of elementary events = 2 [Hearts and diamonds are of red colour]
P(getting a king of red colour) 
(ii) The favourable number of elementary events = 13 [13 card of the spade]
P(getting a spade)
(iii) The favourable number of elementary events = 6 [2Kings , 2Queens and 2 jacks]
P(getting a spade) 
Q5. A bag contains 5 white , 6 red and 4 green marbles . One marble is drawn at random from the bag .
What the probability that the marble drawn is not red ? [SEBA 2013]
Solution : Total number of marbles 
P(not red marbles) 
Q6. A bag contains a red ball , a blue ball and a yellow ball, all the balls being of the same size .
Kritika takes out a ball from the bag without looking into it . What is the probability that she
takes out the –
(i) yellow ball ? (ii) red ball ? (iii) blue ball ?
Solution : Total number of balls 
(i) P(getting yellow ball) 
(ii) P(getting red ball)
(iii) P(getting blue ball)
Q7. Two different dice are tossed together . Find the probability of getting - [CBSE 2014]
(i) same number on both dice (i.e. a doublet) .
(ii) a multiple of 3 as the sum .
Solution : Total number of possible outcome 
.
(i) The total number of elementary events 
P(getting the number on each die is even) 
(ii) The total number of elementary events = 12 .
P(getting a multiple of 3 as the sum) 
Q8. From all the two digit numbers, a number is chosen at random . Find the probability that the
chosen number is a multiple of 7 . [2017C]
Solution : The total number of possible outcome 
The favourable number of elementary events 
P(getting the number is a multiple of 7) 
Q9. A bag contains 25 cards numbered from 1 to 25 . A card is drawn at random from the bag . Find the
probability that the number on the drawn card is : [2015 Delhi]
(i) divisible by 3 or 5 . (ii) a perfect square number .
Solution : The total number of the cards = 25 .
(i) The favourable number of elementary events 
P( getting the number divisible by 3 or 5) 
(ii) The favourable number of elementary events 
P(getting a perfect square number) 
SECTION = C [3 Marks]
Q1. All red face cards are removed from a pack of playing cards . The remaining cards were well shuffled
and then a card is drawn at random from them . Find the probability that the drawn cards is :
(i) a red card (ii) a face card (iii) a card of clubs [2015 Delhi]
Solution : Total number of possible outcome 
[6 red face card are removed from the pack]
(i) The total number of a red card 
P(getting a red card) 
(ii) The total number of a face card = 
P(getting a face card) 
(iii) The total number of a card of clubs
P(getting a card of clubs) 
Q2. Three different coins are tossed together .Find the probability of getting : [2016]
(i) exactly two heads (ii) at least two heads
Solution : Total number of possible outcome 
(i) The favourable number of elementary events 
P(getting the exactly two heads)
(ii) The favourable number of elementary events 
P(getting at least two heads) 
Q3. 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 : [CBSE 2014F]
(i) not divisible by 3 .
(ii) a prime number greater than 7 .
(iii) not a perfect square number .
Solution : Total number of possible outcome 
.
(i) The favourable number of elementary events 
P(not divisible by 3) 
(ii) The favourable number of elementary events 
P(getting a prime number greater than 7) 
(iii) The favourable number of elementary events 
P(not a perfect square number) 
Q4. A piggy bank contains hundred 50 p coins , fifty Rs. 1 coins , twenty Rs. 2 coins and ten Rs. 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 50 p coin ? (ii) will not be a Rs. 5 coin ?
Solution : Total number of coins 
(i) The total number of a 50 p coins = 100 .
P(getting a 50 p coin) 
(ii) The total number of a Rs. 5 coins 
P(getting a Rs. 5 coin) 
Q5. A number 
is selected at random from the numbers 1 , 2 , 3 and 4 . Another number 
is selected
at random from the numbers 1 , 4 , 9 and 16 . Find the probability that product of and 
is less
than 16 . [2016]
Solution : The total number of possible outcome = 16 .
The total number of elementary events 
P(getting the product of and is less than 16) 
Q7. A box contains cards, number from 1 to 90 . A card is drawn at random from the box. Find the
probability that the selected card bears :
(i) a perfect square number (ii) a prime number between 8 to 40 .
Solution : Total number of possible outcome 
.
(i) The total number of a perfect square number from 1 to 90 = 9 [1,4,9,16,25,36,49,64,81]
P(getting a perfect square number) 
(ii) The total number of a prime number between 8 to 40 = 8 [11,13,17,19,23,29,31,37]
P(getting a prime number between 8 to 40) 
Q8. 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 ?
Solution : The total number of possible outcome = 5 [ten, jack ,queen, king and ace]
(i) The number of elementary events = 1 [ Queen only]
P( getting the queen) 
(ii) The total number of elementary events = 4 [ The queen has removed]
(a) P(getting an ace) 
(b) P(getting a queen) 
Q9. A box contains cards bearing numbers from 6 to 70 . If one card is drawn at random from the box ,
find the probability that it bears : [CBSE 2015F]
(i) a one digit number. (ii) a number divisible by 5 .
(iii) an odd number less than 30 (iv) a composite number between 50 and 70 .
Solution : Total number of possible outcome 
(i) Total number of a one digit number 
[6 , 7 , 8 , 9]
P(getting a one digit number) 
(ii) Total number of a number divisible by 5 [10,15,20,25,30,35,40,45,50,55,60,65,70]
P(getting a number divisible by 5) 
(iii) Total number of an odd number less than 30 
[7,9,11,13,15,17,19,21,23,25,27,29]
P(getting an odd number less than 30) 
.
(iv) Total number of a composite number between 50 and 70 
[ Composite number between 50 and 70 are 51,52,54,56,57,58,60,62,63,64,65,68,69,70]
P(getting a composite number between 50 and 70) 
Posted 5 years ago