Probability
Class 8th Mathematics RS Aggarwal Solution
- A coin is tossed. What are all possible outcomes? (i) Two coins are tossed…
- In a single throw of a coin, what is the probability of getting a tail?…
- In a single throw of two coins, find the probability of getting (i) both tails,…
- A bag contains 4 white and 5 blue balls. They are mixed thoroughly and one ball…
- A bag contains 5 white, 6 red and 4 green balls. One ball is drawn at random.…
- In a lottery, there are 10 prizes and 20 blanks. A ticket is chosen at random.…
- It is known that a box of 100 electric bulbs contains 8 defective bulbs. One…
- A die is thrown at random. Find the probability of getting (i) 2 (ii) a number…
- In a survey of 200 ladies, it was found that 82 like coffee while 118 dislike…
- A box contains 19 balls bearing numbers 1, 2, 3 ..., 19 respectively. A ball…
- One card is drawn at random from a well-shuffled deck of 52 cards. Find the…
- One card is drawn at random from a well-shuffled deck of 52 cards.…
- In a spinning wheel, there are 3 white and 5 green sectors. It is spinned. What…
- 8 cards are numbered as 1, 2, 3, 4, 5, 6, 7, 8 respectively. They are kept in a…
- Two coins are tossed simultaneously. What is the probability of getting one…
- A bag contains 3 white and 2 red balls. One ball is drawn at random. What is…
- A die is thrown. What is the probability of getting 6?A. 1 B. 1/6 C. 6/1 D.…
- A die is thrown. What is the probability of getting an even number?A. 1/2 B.…
- From a well-shuffled deck of 52 cards, one card is drawn at random. What is the…
- From a well-shuffled deck of 52 cards, one card is drawn at random. What is the…
Exercise 24a
Question 1.A coin is tossed. What are all possible outcomes?
(i) Two coins are tossed simultaneously. What are all possible outcomes?
(ii) A die is thrown. What are all possible outcomes?
(iii) From a well-shuffled deck of 52 cards, one card is drawn at random. What is the number of all possible outcomes?
Answer:
(i) A coin has two sides a head(H) and a tail(T).
There are Xm possible outcomes.
[Where X is number of outcomes when a coin is tossed and m is number of coins.]
That is 21 = 2 and they are H, T.
All possible outcomes are H, T.
(ii) A coin has two sides a head(H) and a tail(T), and there are two such coins.
There are Xm possible outcomes.
[Where X is number of outcomes when a coin is tossed and m is number of coins.]
That is 22 = 4 and they are HH, HT, TH, TT
All possible outcomes are HH, HT, TH, TT.
(iii) A die has 6 faces and they are 1, 2, 3, 4, 5, 6
All possible outcomes are 1, 2, 3, 4, 5, 6.
(iv) A deck of cards have a total of 52 cards.
Number of possible outcomes are 52.
Question 2.
In a single throw of a coin, what is the probability of getting a tail?
Answer:
A coin has two sides a head(H) and a tail(T).
All possible outcomes are H, T.
Total number of outcomes = 2
Chances of getting a tail = 1
Probability P() = 
Probability of getting a tail P(T) 
= 
Question 3.
In a single throw of two coins, find the probability of getting (i) both tails, (ii) at least 1 tail,(iii) at the most 1 tail.
Answer:
(i) A coin has two sides a head(H) and a tail(T), and there are two such coins.
There are Xm possible outcomes.
That is 22 = 4 and they are HH, HT, TH, TT
All possible outcomes are HH, HT, TH, TT.
Total number of outcomes = 4
Chances of getting 2 tails = 1, that is TT
Probability P() =
Probability of getting a tail P(both T) = 
= 
(ii) A coin has two sides a head(H) and a tail(T), and there are two such coins.
There are Xm possible outcomes.
That is 22 = 4 and they are HH, HT, TH, TT
All possible outcomes are HH, HT, TH, TT.
Total number of outcomes = 4
Chances of getting atleast one tail = 3, that is HT, TH, TT.
Probability P() =
Probability of getting a tail P(atleast 1 T) = 
=
(iii) A coin has two sides a head(H) and a tail(T), and there are two such coins.
There are Xm possible outcomes.
That is 22 = 4 and they are HH, HT, TH, TT
All possible outcomes are HH, HT, TH, TT.
Total number of outcomes = 4
Chances of getting atmost 1 tail = 3, that is HT, TH, TT.
Probability P() =
Probability of getting a tail P(atmost 1 T) = 
=
Question 4.
A bag contains 4 white and 5 blue balls. They are mixed thoroughly and one ball is drawn at random. What is the probability of getting (i) a white ball? (ii) a blue ball?
Answer:
(i) Total number of balls bag containing is: 4 white + 5 blue = 9 balls
Number of white balls = 4.
Probability P() =
Probability of getting a white ball P(W) = 
= 
(ii) Total number of balls bag containing is: 4 white + 5 blue = 9 balls
Number of blue balls = 5.
Probability P() =
Probability of getting a blue ball P(B) = 
= 
Question 5.
A bag contains 5 white, 6 red and 4 green balls. One ball is drawn at random. What is the probability that the ball drawn is (i) green?(ii) white? (iii)non-red?
Answer:
(i).
Total number of balls bag containing is: 5 white + 6 red + 4 green = 15 balls
Number of green balls = 4.
Probability P() =
Probability of getting a Green ball P(G) = 
= 
(ii).
Total number of balls bag containing is: 5 white + 6 red + 4 green = 15 balls
Number of white balls = 5.
Probability P() =
Probability of getting a white ball P(W) = 
= 
= 
(iii).
Total number of balls bag containing is: 5 white + 6 red + 4 green = 15 balls
Number of outcomes (No Red) = 5 + 4 = 9, that is 5 white balls + 4 Green balls.
Probability P() =
Probability of getting a Green ball P(G) = 
=
= 
Question 6.
In a lottery, there are 10 prizes and 20 blanks. A ticket is chosen at random. What is the probability of getting a prize?
Answer:
Total number of lottery Tickets = 30
Number of lottery tickets having a prize = 10
Probability P() =
Probability of getting a prized lottery ticket P(p) = 
= 
=
Question 7.
It is known that a box of 100 electric bulbs contains 8 defective bulbs. One bulb is taken out at random from the box. What is the probability that the bulb drawn is (i) defective? (ii) non-defective?
Answer:
(i) Total number of electric bulbs = 100
Number of defective bulbs = 8
Probability P() =
Probability of getting a defective bulbs P(d bulbs) = 
= 
= 
(ii) Total number of electric bulbs = 100
Number of Non-defective bulbs = 100-8 = 92 (Number of electric bulbs – Number of defective bulbs)
Probability P() =
Probability of getting a Non- defective bulbs P(bulbs) = 
= 
= 
Question 8.
A die is thrown at random. Find the probability of getting (i) 2 (ii) a number less than 3 (iii) a composite number (iv) a number not less than 4.
Answer:
(i) Total number of outcomes = 6 (they are 1,2,3,4,5,6)
Chances of getting 2 on the die = 1
Probability P() =
Probability of getting 2 on die P(2) = 
= 
(ii) Total number of outcomes = 6 (they are 1,2,3,4,5,6)
Chances of getting a number less than 3 on the die = 2 (They are 1,2)
Probability P() =
Probability of getting a number less than 3 on die P(less than 3)
= 
= 
=
(iii) Total number of outcomes = 6 (they are 1,2,3,4,5,6)
Composite number: A number which is not a prime number or a number which is divisible by numbers other than 1 and the number itself.
Chances of getting a composite number on the die = 2 (They are 4,6)
Probability P() =
Probability of getting a composite number on die the P(composite number)
= = =
(iv) Total number of outcomes = 6 (they are 1,2,3,4,5,6)
Chances of getting a number not less than 4 on the die = 4 (They are 4,5,6)
Probability P() =
Probability of getting a number not less than 4 on die P(not less than 4)
= = 
=
Question 9.
In a survey of 200 ladies, it was found that 82 like coffee while 118 dislike it. From these ladies, one is chosen at random. What is the probability that the chosen lady dislikes coffee?
Answer:
Total number of ladies: 200
Number of ladies who like coffee: 82
Number of ladies who dislike coffee: 118
Probability P() =
Let p( No Coffee) be probability of ladies who dislike coffee
P (No Coffee) = 
P (No Coffee) = 
= 
Question 10.
A box contains 19 balls bearing numbers 1, 2, 3 ..., 19 respectively. A ball is drawn at random from the box. Find the probability that the number on the ball is (i) a prime number (ii) an even number (iii) a number divisible by 3.
Answer:
(i) Total number of ball bearings = 19
Chances of drawing a prime numbered ball = 9 (They are 2,3,5,7,11,13,17,19)
Probability P() =
Probability of drawing a prime numbered ball bearing P(prime ball)
= 
= 
(ii) Total number of ball bearings = 19
Chances of drawing an even numbered ball = 9 (They are 2,4,6,8,10,12,14,16,18)
Probability P() =
Probability of drawing an even numbered ball bearing P(even ball)
= 
= 
(iii) Total number of ball bearings = 19
Chances of drawing a numbered ball which is divisible by 3 =6 (They are 3,6,9,12,15,18)
Probability P() =
Probability of drawing a numbered ball bearing which is divisible by 3 P(ball divisible by 3)
= 
= 
Question 11.
One card is drawn at random from a well-shuffled deck of 52 cards. Find the probability that the card drawn is (i) a king (ii) a spade (iii) a red queen (iv) a black 8.
Answer:
(i) Total number cards in a deck = 52
Number of kings in a deck of cards = 4
Probability P() =
Probability of drawing a king from the deck of cards P(king)
= 
= 
=
(ii) Total number cards in a deck = 52
Number of spades in a deck of cards = 13
Probability P() =
Probability of drawing a spade from the deck of cards P(spade)
= 
= 
=
(iii) Total number cards in a deck = 52
Chances of drawing a Red queen from the deck of cards = 2 (they are queen of hearts and queen of diamonds)
Probability P() =
Probability of drawing a Red queen from the deck of cards P(Red queen)
= 
= 
=
(iv) Total number cards in a deck = 52
Chances of drawing a black 8 from the deck of cards = 2 (they are 8 of clubs and 8 of spades)
Probability P() =
Probability of drawing a black 8 from a deck of cards P(black 8)
= 
= =
Question 12.
One card is drawn at random from a well-shuffled deck of 52 cards. Find the probability that the card drawn is (i) a 4 (ii) a queen (iii) a black card.
Answer:
(i) Total number cards in a deck = 52
Number of 4’s in a deck of cards = 4
Probability P() =
Probability of drawing a 4 numbered card from the deck of cards P(4)
= 
= =
(ii) Total number cards in a deck = 52
Number of Queens in a deck of cards = 4
Probability P() =
Probability of drawing a queen from the deck of cards P(queen)
= 
= =
(iii) Total number cards in a deck = 52
Number of black cards in a deck of cards = 26 (13 spades and 13 clubs)
Probability P() =
Probability of drawing a black card from the deck of cards P(black)
= 
= 
=
Exercise 24b
Question 1.In a spinning wheel, there are 3 white and 5 green sectors. It is spinned. What is the probability of getting a green sector?
A. 
B. 
C. 
D. 
Answer:
Total number sectors = 8
Number of green sectors = 5
Probability P() =
Probability of getting a green sector P(green) = 
= 
Question 2.
8 cards are numbered as 1, 2, 3, 4, 5, 6, 7, 8 respectively. They are kept in a box and mixed thoroughly. Once card is chosen at random. What is the probability of getting a number less than 4?
A. 
B. 
C.
D. 
Answer:
Total number cards kept in the box = 8
Number of cards having a number less than 4 on it = 3
Probability P() =
Probability of selecting a card with a number less than 4 P(No. less than 4)
= 
= 
Question 3.
Two coins are tossed simultaneously. What is the probability of getting one head and one tail?
A. 
B.
C.
D. 
Answer:
All possible outcomes are HH, HT, TH, TT.
Total number of outcomes = 4
Chances of getting one head and one tail = 3, that is TH and HT
Probability P() =
Probability of getting a tail P(both T) = 
= 
= 
Question 4.
A bag contains 3 white and 2 red balls. One ball is drawn at random. What is the probability that the ball drawn is red?
A.
B.
C.
D. 
Answer:
Total number of balls bag containing is: 3 white + 2 red = 5 balls
Number of red balls = 2
Probability P() =
Probability of getting a red ball P(R) = 
= 
Question 5.
A die is thrown. What is the probability of getting 6?
A. 1
B. 
C. 
D. none of these
Answer:
Total number of outcomes = 6 (they are 1,2,3,4,5,6)
Chances of getting 6 on the die = 1
Probability P() =
Probability of getting 6 on die P(6) = 
=
Question 6.
A die is thrown. What is the probability of getting an even number?
A.
B.
C. 
D.
Answer:
Total number of outcomes = 6 (they are 1,2,3,4,5,6)
Chances of getting a even number on the die = 3 they are (2,4,6)
Probability P() =
Probability of getting even number on the die P(even) = 
=
Question 7.
From a well-shuffled deck of 52 cards, one card is drawn at random. What is the probability that the drawn card is a queen?
A. 
B. 
C. 
D. 
Answer:
Total number cards in a deck = 52
Number of Queens in a deck of cards = 4
Probability P() =
Probability of drawing a queen from the deck of cards P(queen)
= = =
Question 8.
From a well-shuffled deck of 52 cards, one card is drawn at random. What is the probability that the drawn card is a black 6?
A. 
B.
C.
D.
Answer:
Total number cards in a deck = 52
Chances of drawing a black 6 from the deck of cards = 2 (they are 8 of clubs and 8 of spades)
Probability P() =
Probability of drawing a black 6 from a deck of cards P(black 6)
= 
= =