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Page No 282:

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:

(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.

Page No 282:

Question 2:

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

Answer:

The possible outcomes in a coin toss are H and T.
Total number of outcomes = 2
Number of tails = 1
∴ Ptail=12

Page No 282:

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:

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
∴ Pboth tails=14

 
(ii) Getting at least 1 tail means HT, TH and TT.
​With at least one tail, total number of outcomes = 3
∴ Pat least 1 tail=34

(iii) Getting at most 1 tail means HH, HT and TH.
The number of outcomes for at most 1 tail = 3
∴​Pat most 1 tail=34

Page No 282:

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:

Total number of balls = 4+5=9
(i) Number of white balls = 4
∴​ Pwhite ball=49

Number of blue balls = 5
∴​ Pblue ball=59

Page No 282:

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:

Total number of balls =5+6+4=15
(i) Number of green balls = 4
∴​ Pgreen ball=415

(ii) Number of white balls = 5
∴​ Pwhite ball=515=13

(iii) Number of balls that are not red (i.e., 5 white and 4 green)= 9
∴​ Pnon-red balls=915=35

Page No 282:

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 tickets =10+20=30

Number of prize tickets = 10

∴​ Pgetting a prize=1030=13

Page No 282:

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:

Total number of bulbs in the box = 100
(i) Number of defective bulbs = 8
∴​ Pdefective bulb=8100=225

(ii) Number of functioning bulbs= 100-8=92
∴​ Pnon-defective bulb=92100=2325



Page No 283:

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:

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

(i) ∴​ Pgetting 2=16

(ii) The numbers less than 3 are 1 and 2.
      Number of possible outcomes = 2
      ∴​ Pgetting a number<3=26=13

(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
∴​ Pgetting a composite number=26=13

 
(iv) A number not less than 4 can includes 4, 5 or 6.
      Number of outcomes = 3  
      ∴Pgetting a number not less than 4=36=12

Page No 283:

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 surveyed =200

Number of ladies who dislike coffee =118

If chosen randomly, P(a lady that dislikes coffee) = 118200=59100

Page No 283:

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:

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   
     ∴ Pprime number=819


(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
     ∴ Peven number=919

(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
       ∴ Pnumber divisble by 3=619
 
 

 

Page No 283:

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:

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
∴ Pking=452=113

(ii) There is a total of 13 spades cards.
Number of spades=13
Pspades=1352=14
(iii) There are 2 red queens in a pack (queen of hearts and queen of diamonds)
Number of red queens =2
Pred queen=252=126

 
(iv) There are 2 black 8s in a pack (8 of cloves and 8 of spades)
Number of black 8s =2
Pblack 8=252=126
 
 

Page No 283:

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:

Total number of possible outcomes =52
(i) There are 4 cards of with the number 4 (4 of hearts, 4 of diamonds, 4 of spades and 4 of cloves)
∴ P4 card=452=113
(ii) There are 4 queens in a pack of cards (queen of hearts, queen of diamonds, queen of spades and queen of cloves)
∴ Pqueen=452=113
(iii) There are a total of 26 black cards (13 spade cards and 13 clove cards)
Pblack card=2652=12

Page No 283:

Question 1:

Tick (✓) the correct answer:
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) 53
(b) 58
(c) 15
(d) 38

Answer:

(b) 58

The wheel has a total of 5+3=8 sectors.
Number of green sectors = 5
Now, Pgetting a green sector=58

Page No 283:

Question 2:

Tick (✓) the correct answer:
8 cards are numbered as 1, 2, 3, 4, 5, 6, 7, 8 respectively. They are kept in a box and mixed thoroughly. One card is chosen at random. What is the probability of getting a number less than 4?
(a) 12
(b) 34
(c) 38
(d) 35

Answer:

(c) 38

Total number of cards =8
Number of cards with numbers less than 4 =3 (cards with numbers 1, 2 and 3)
Now, Pgetting a number less than 4=38

Page No 283:

Question 3:

Tick (✓) the correct answer:
Two coins are tossed simultaneously. What is the probability of getting one head and one tail?
(a) 14
(b) 12
(c) 34
(d) 23

Answer:

(b) 12

When two coins are tossed, the possible outcomes are HH, HT, TH and TT.
​Total number of outcomes =4
Number of outcomes with one head and one tail =2
Now, Pone head and one tail=24=12

Page No 283:

Question 4:

Tick (✓) the correct answer:
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) 12
(b) 23
(c) 15
(d) 25

Answer:

(d) 25

Total number of outcomes =5
Number of red balls =2
Now, Pred ball=25

Page No 283:

Question 5:

Tick (✓) the correct answer:
A die is thrown. What is the probability of getting 6?
(a) 1
(b) 16
(c) 61
(d) none of these

Answer:

(b) 16

The possible outcomes are 1, 2, 3, 4, 5 and 6.
Total number of outcomes =6
Now, P(getting 6) = 16

Page No 283:

Question 6:

Tick (✓) the correct answer:
A die is thrown. What is the probability of getting an even number?
(a) 12
(b) 23
(c) 56
(d) 16

Answer:

(a) 12

Total number of outcomes =6 (Numbers: 1, 2, 3, 4, 5 and 6)
The even numbers are 2, 4, and 6.
Number of favourable outcomes =3
Now, Peven number=36=12



Page No 284:

Question 7:

Tick (✓) the correct answer:
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) 14
(b) 152
(c) 113
(d) 126

Answer:

(c) 113

Total number of cards =52
Number of queens = 4 (i.e., queen of hearts, queen of diamonds, queen of cloves and queen of spades)
Now, P(queen)=452=113

Page No 284:

Question 8:

Tick (✓) the correct answer:
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) 326
(b) 126
(c) 113
(d) 152

Answer:

(b) 126

Total number of cards = 52
Total number of black 6 cards = 2   (6 of spades, 6 of cloves)
Now, P(black 6)=252=126



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