Probability PART 3 - X NCERT

Exercise – 15.1
6. A bag contains lemon flavoured candies only. Malini takes
out one candy without looking into the bag. What is the
probability that she takes out (i) an orange flavoured candy?
(ii) a lemon flavoured candy?
Solution :
P( an orange flavoured candy) =
= 0 (Impossible event)
P( a lemon flavoured candy) =
= 1 (Sure Event)

7. It is given that in 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 :
Given that,
Probability of 2 students not having the same birthday is
0.992
P(E) = 0.992
Probability of 2 students having the same birthday
P( ) = 1 – P(E) = 1 – 0.992 = 0.008E

10. A piggy bank contains hundred 50p 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:
No. of 50 paise coins = 100
No. of Rs. 1 coins = 50
Total no. of coins in the piggy bank = 100 + 50 +20 +5
= 175
i) P( the coin will be a 50 p coin) =
ii) P( the coin will not be a Rs. 5 coin) =
100 4
175 7

170 34
175 35


11. 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 :
No. of male fish = 5
No. of female fish = 8
Total no. of fishes = 8 + 5 = 13
Now,
P( fish taken out is a male fish) =
=
5
13

12. 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 (see Fig. 15.5 ),
and these are equally likely outcomes. What is the probability that it
will point at (i) 8 ? (ii) an odd number? (iii) a number greater than 2?
(iv) a number less than 9?
Solution :
Total no. of possible outcomes are 8
P(E) =
i) P( it will point at 8) =
ii) P( will point at an odd number) =
iii) P( will point at a number greater than 2) =
iv) P( will point at a number less than 9) =
1
8 4 1
8 2

6 3
8 4

8
1
8


13. A die is thrown once. Find the probability of getting
(i) a prime number; (ii) a number lying between
2 and 6; (iii) an odd number.
Solution :
Throwing a die is an experiment
Possible outcomes are 1 or 2 or 3 or 4 or 5 or 6
i) Favourable outcomes to get a prime number are 2,3 and 5
P(getting a prime number) =
ii) Favourable outcomes to get a number lying between 2 & 6
are 3, 4 and 5
P( getting a number lying between 2 and 6) =
iii) Favourable outcomes to get an odd number are 1, 3 and 5
P( getting a number is an odd number) =
3 1
6 2

3 1
6 2

3 1
6 2


14. 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 face card (iii)
a red face card (iv) the jack of hearts (v) a spade (vi) the queen of
diamonds
Solution :
Total no. of cards = 52
i) P(getting a king of red colour) =
ii) P( getting a face card ) =
iii) P( getting a red face card) =
iv) P( getting a jack of hearts) =
v) P( getting a spade card) =
vi) P( getting a queen of diamonds) =
2 1
52 26

12 3
52 13

6 3
52 26

1
52
13 1
52 4

1
52

15. 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 :
Given that,
Total no. of cards = 5 (Ten, Jack, Queen, King and Ace of
diamond)
i) P( card is the queen) =
ii) Total no. of cards = 4 (Ten, Jack, King & Ace of diamond)
a) P( an ace card) =
b) P( a queen card) = 0
1
5
1
4

17. (i) A lot of 20 bulbs contain 4 defective ones. One bulb is
drawn at random from the lot. What is the probability
that this bulb is defective?
(ii) Suppose the bulb drawn in (i) is not defective and is
not replaced. Now one bulb is drawn at random from
the rest. What is the probability that this bulb is not
defective ?
Solution :
i) Total no. of bulbs in a lot = 20
No. of defective bulbs = 4
No. of bulbs are in good condition = 20 – 4 = 16
P(taking a defective bulb) =
=
4 1
20 5


ii) According to the problem in case (i), bulb drawn one was
not defective and the bulb kept aside.
Now,
No. of bulbs are in good condition = 16 – 1 = 15
P(taking a not defective bulb) =
=
15
19

18. 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.
Solution :
Total no. of discs are in the box = 90
i) Total no. of two – digit numbers are in the box = 81
(i.e. 10,11,12,13,14, …………. 89, 90)
P(getting a 2 – digit number) =
ii) Total no. of perfect square numbers = 9
(i.e. 1,4,9,16,25,36,49,64 & 81)
P(getting a perfect square number) =
iii) Total no. of numbers divisible by 5 = 18
(i.e. 5,10,15,20,………,85,90)
P(getting a number divisible by 5) =
81 9
90 10

9 1
90 10

18 1
90 5


23. A game consists of tossing a one rupee coin 3 times and
noting its outcome each time. Hanif wins if all the tosses give
the same result i.e., three heads or three tails, and loses
otherwise. Calculate the probability that Hanif will lose the
game.
Solution :
Tossing a one rupee coin 3 times is an experiment
Possible outcomes are : 8
They are : (H,H,H), (H,H,T), (H,T,H),
(H,T,T), (T, H, H), (T,H,T), (T,T,H),
(T,T,T).
Favourable outcomes to win the game
are (H,H,H) & (T,T,T)
P(E) = P( ) = 1 -
1 TIME 2 TIME 3 TIME
H H H
H H T
H T H
H T T
T H H
T H T
T T H
T T T
2 1
8 4
 E
1 3
4 4


24. A die is thrown twice. What is the probability that
(i) 5 will not come up either time?
(ii) 5 will come up at least Once?
[Hint : Throwing a die twice and throwing two dice
simultaneously are treated as the same experiment]
Solution :
Throwing a die twice is an experiment
Total no. of possible outcomes are 36
1 2 3 4 5 6
1 (1, 1) (1 ,2) (1 ,3) (1, 4) (1 , 5) (1 ,6)
2 (2 , 1) (2 , 2) (2 , 3) (2 , 4) (2 , 5) (2 , 6)
3 (3 , 1) (3 , 2) (3 , 3) (3 , 4) (3 , 5) (3 , 6)
4 (4 , 1) (4 , 2) (4 , 3) (4 , 4) (4 , 5) (4 , 6)
5 (5 , 1) (5 , 2) (5 , 3) (5 , 4) (5 , 5) (5 , 6)
6 (6 , 1) (6 , 2) (6 , 3) (6 , 4) (6 , 5) (6 , 6)

i) No. of favourable outcomes for 5 will not come up either time
(1,1),(1,2),(1,3),(1,4),(1,6),(2,1),(2,2),(2,3),(2,4),(2,6),
(3,1),(3,2),(3,3),(3,4),(3,6),(4,1),(4,2),(4,3),(4,4),(4,6)
(6,1),(6,2),(6,3),(6,4),(6,6) Total 25
P(5 will not come up either time) =
ii) No. of favourable outcomes for 5 will come up at least once
(1,5),(2,5),(3,5),(4,5),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,5)
Total = 11
P( 5 will come up at least once) =
25
36
11
36

Probability PART 3 - X NCERT

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Probability PART 3 - X NCERT