RS Aggarwal solution class 8 chapter 25 Probability Exercise 25A

Exercise 25A

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Q1 | Ex-25A | Class 8 | RS AGGARWAL | chapter 25 | Probability

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Question 1:

(i) A coin is tossed. What are all possible outcomes?
(ii) Two coins are tossed simultaneously. What are all possible outcomes?
(iii) A die is thrown. What are all possible outcomes?
(iv) From a  well-shuffled deck of 52 cards, one card is drawn at random. What is the number of all possible outcomes?

Answer 1:

(i) The possible outcomes are head (H) and tail (T).

(ii) The possible outcomes are HH, HT, TH and TT.

(iii) The possible outcomes are 1, 2, 3, 4, 5 and 6.

(iv) The total number of possible outcomes is 52.

Q2 | Ex-25A | Class 8 | RS AGGARWAL | chapter 25 | Probability

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Question 2:

In a single throw of a coin, what is the probability of getting a tail?

Answer 2:

The possible outcomes in a coin toss are H and T.
Total number of outcomes = 2
Number of tails = 1
∴ 

Q3 | Ex-25A | Class 8 | RS AGGARWAL | chapter 25 | Probability

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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 3:

The outcomes when two coins are tossed are HH, HT, TH and TT.
i.e., total no. of possible outcomes = 4

(i) Getting both tails means TT.
Number of outcomes with two tails = 1
∴ 

(ii) Getting at least 1 tail means HT, TH and TT.
​With at least one tail, total number of outcomes = 3
∴ 

(iii) Getting at most 1 tail means HH, HT and TH.
The number of outcomes for at most 1 tail = 3
∴​${\mathrm{P}}_{\left(\mathrm{at} \mathrm{most} 1 \mathrm{tail}\right)}=\frac{3}{4}$

Q4 | Ex-25A | Class 8 | RS AGGARWAL | chapter 25 | Probability

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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 4:

Total number of balls
(i) Number of white balls = 4
∴​ 

Number of blue balls = 5
∴​ 

Q5 | Ex-25A | Class 8 | RS AGGARWAL | chapter 25 | Probability

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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 5:

Total number of balls $=5+6+4=15$
(i) Number of green balls = 4
∴​ ${\mathrm{P}}_{\left(\mathrm{green} \mathrm{ball}\right)}=\frac{4}{15}$

(ii) Number of white balls = 5
∴​ ${\mathrm{P}}_{\left(\mathrm{white} \mathrm{ball}\right)}=\frac{5}{15}=\frac{1}{3}$

(iii) Number of balls that are not red (i.e., 5 white and 4 green)$= 9$
∴​ ${\mathrm{P}}_{\left(\mathrm{non}-\mathrm{red} \mathrm{balls}\right)}=\frac{9}{15}=\frac{3}{5}$

Q6 | Ex-25A | Class 8 | RS AGGARWAL | chapter 25 | Probability

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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 6:

Total number of tickets $=10+20=30$

Number of prize tickets = 10

∴​ 

Q7 | Ex-25A | Class 8 | RS AGGARWAL | chapter 25 | Probability

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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 7:

Total number of bulbs in the box = 100
(i) Number of defective bulbs = 8
∴​ 

(ii) Number of functioning bulbs= $100-8=92$
∴​ 

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Q8 | Ex-25A | Class 8 | RS AGGARWAL | chapter 25 | Probability

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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 8:

The possible outcomes when a dice is thrown at random are 1, 2, 3, 4, 5 and 6.
Total number of outcomes = 6

(i) ∴​ 

(ii) The numbers less than 3 are 1 and 2.
      Number of possible outcomes = 2
      ∴​ 

(iii) A composite number is defined as a number with at least one positive divisor other than itself and unity.
In a dice, 4 and 6 are composite numbers.
Number of possible outcomes = 2
∴​ 

(iv) A number not less than 4 can includes 4, 5 or 6.
      Number of outcomes = 3 
      ∴

Q9 | Ex-25A | Class 8 | RS AGGARWAL | chapter 25 | Probability

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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 9:

Total number of ladies surveyed 

Number of ladies who dislike coffee 

If chosen randomly, 

Q10 | Ex-25A | Class 8 | RS AGGARWAL | chapter 25 | Probability

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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 10:

Total number of possible outcomes$=19$
(i) The prime numbers between 1 and 19 are 2, 3, 5, 7, 11, 13, 17 and 19.
     Total number of primes $=8$  
     ∴

(ii) The even numbers between 1 and 19 are 2, 4, 6, 8, 10 ,12, 14, 16 and 18.

      Total number of even numbers$=6$
     ∴

(iii) The numbers between 1 and 19 which are divisible by 3 are 3, 6, 9, 12, 15 and 18.
       Total number of possible outcomes = 6
       ∴

Q11 | Ex-25A | Class 8 | RS AGGARWAL | chapter 25 | Probability

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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 11:

Total number of possible outcomes$=52$
(i) There are 4 kings cards (king of hearts, king of diamonds, king of spades and king of cloves)
Number of kings$=4$
∴ 

(ii) There is a total of 13 spades cards.
Number of spades$=13$
∴
(iii) There are 2 red queens in a pack (queen of hearts and queen of diamonds)
Number of red queens $=2$
∴

(iv) There are 2 black 8s in a pack (8 of cloves and 8 of spades)
Number of black 8s $=2$
∴

Q12 | Ex-25A | Class 8 | RS AGGARWAL | chapter 25 | Probability

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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 12:

Total number of possible outcomes
(i) There are 4 cards of with the number 4 (4 of hearts, 4 of diamonds, 4 of spades and 4 of cloves)
∴ 
(ii) There are 4 queens in a pack of cards (queen of hearts, queen of diamonds, queen of spades and queen of cloves)
∴ 
(iii) There are a total of 26 black cards (13 spade cards and 13 clove cards)
∴