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#### Page No 282:

(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:

The possible outcomes in a coin toss are H and T.
Total number of outcomes = 2
Number of tails = 1
∴ ${\mathrm{P}}_{\left(\mathrm{tail}\right)}=\frac{1}{2}$

#### Page No 282:

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
∴​

#### Page No 282:

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

Number of blue balls = 5
∴​

#### Page No 282:

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

(ii) Number of white balls = 5
∴​

(iii) Number of balls that are not red (i.e., 5 white and 4 green)
∴​

#### Page No 282:

Total number of tickets $=10+20=30$

Number of prize tickets = 10

∴​

#### Page No 282:

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

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

#### Page No 283:

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
∴

#### Page No 283:

Total number of ladies surveyed $=200$

Number of ladies who dislike coffee $=118$

If chosen randomly,

#### Page No 283:

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
∴

#### Page No 283:

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$=4$
∴ ${\mathrm{P}}_{\left(\mathrm{king}\right)}=\frac{4}{52}=\frac{1}{13}$

(ii) There is a total of 13 spades cards.
Number of spades$=13$
${\mathrm{P}}_{\left(\mathrm{spades}\right)}=\frac{13}{52}=\frac{1}{4}$
(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 $=2$

#### Page No 283:

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)
∴
(ii) There are 4 queens in a pack of cards (queen of hearts, queen of diamonds, queen of spades and queen of cloves)
∴ ${\mathrm{P}}_{\left(\mathrm{queen}\right)}=\frac{4}{52}=\frac{1}{13}$
(iii) There are a total of 26 black cards (13 spade cards and 13 clove cards)

#### Page No 283:

(b) $\frac{5}{8}$

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

#### Page No 283:

(c) $\frac{3}{8}$

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

#### Page No 283:

(b) $\frac{1}{2}$

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 $=2$

#### Page No 283:

(d) $\frac{2}{5}$

Total number of outcomes $=5$
Number of red balls $=2$

#### Page No 283:

(b) $\frac{1}{6}$

The possible outcomes are 1, 2, 3, 4, 5 and 6.
Total number of outcomes $=6$
Now,

#### Page No 283:

(a) $\frac{1}{2}$

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,

#### Page No 284:

(c) $\frac{1}{13}$

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

#### Page No 284:

(b) $\frac{1}{26}$