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#### Page No 257:

#### 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 257:

#### 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

∴ ${\mathrm{P}}_{\left(\mathrm{tail}\right)}=\frac{1}{2}$

#### Page No 257:

#### 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

∴ ${\mathrm{P}}_{\left(\mathrm{both}\mathrm{tails}\right)}=\frac{1}{4}$

*HT, TH*and

*TT*.

With at least one tail, total number of outcomes = 3

∴ ${\mathrm{P}}_{\left(\mathrm{at}\mathrm{least}1\mathrm{tail}\right)}=\frac{3}{4}$

(iii) Getting at most 1 tail means

*HH, HT*and

*TH*.

The number of outcomes for at most 1 tail = 3

∴${\mathrm{P}}_{\left(\mathrm{at}\mathrm{most}1\mathrm{tail}\right)}=\frac{3}{4}$

#### Page No 257:

#### 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

∴ ${\mathrm{P}}_{\left(\mathrm{white}\mathrm{ball}\right)}=\frac{4}{9}$

Number of blue balls = 5

∴ ${\mathrm{P}}_{\left(\mathrm{blue}\mathrm{ball}\right)}=\frac{5}{9}$

#### Page No 257:

#### 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

∴ ${\mathrm{P}}_{\left(\mathrm{green}\mathrm{ball}\right)}=\frac{4}{15}$

(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)$=9$

∴ ${\mathrm{P}}_{\left(\mathrm{non}-\mathrm{red}\mathrm{balls}\right)}=\frac{9}{15}=\frac{3}{5}$

#### Page No 257:

#### 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

∴ ${\mathrm{P}}_{\left(\mathrm{getting}\mathrm{a}\mathrm{prize}\right)}=\frac{10}{30}=\frac{1}{3}$

#### Page No 257:

#### 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

∴ ${\mathrm{P}}_{\left(\mathrm{defective}\mathrm{bulb}\right)}=\frac{8}{100}=\frac{2}{25}$

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

∴ ${\mathrm{P}}_{\left(\mathrm{non}-\mathrm{defective}\mathrm{bulb}\right)}=\frac{92}{100}=\frac{23}{25}$

#### Page No 258:

#### 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) ∴ ${\mathrm{P}}_{\left(\mathrm{getting}2\right)}=\frac{1}{6}$

(ii) The numbers less than 3 are 1 and 2.

Number of possible outcomes = 2

∴ ${\mathrm{P}}_{\left(\mathrm{getting}\mathrm{a}\mathrm{number}3\right)}=\frac{2}{6}=\frac{1}{3}$

(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

∴ ${\mathrm{P}}_{\left(\mathrm{getting}\mathrm{a}\mathrm{composite}\mathrm{number}\right)}=\frac{2}{6}=\frac{1}{3}$

Number of outcomes = 3

∴${\mathrm{P}}_{\left(\mathrm{getting}\mathrm{a}\mathrm{number}\mathrm{not}\mathrm{less}\mathrm{than}4\right)}=\frac{3}{6}=\frac{1}{2}$

#### Page No 258:

#### 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, ${\mathrm{P}}_{(\mathrm{a}\mathrm{lady}\mathrm{that}\mathrm{dislikes}\mathrm{coffee})}=\frac{118}{200}=\frac{59}{100}$

#### Page No 258:

#### 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 $=8$

∴ ${\mathrm{P}}_{\left(\mathrm{prime}\mathrm{number}\right)}=\frac{8}{19}$

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

∴ ${\mathrm{P}}_{\left(\mathrm{even}\mathrm{number}\right)}=\frac{9}{19}$

(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

∴ ${\mathrm{P}}_{\left(\mathrm{number}\mathrm{divisble}\mathrm{by}3\right)}=\frac{6}{19}$

#### Page No 258:

#### 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$=4$

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

(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 $=2$

∴ ${\mathrm{P}}_{\left(\mathrm{red}\mathrm{queen}\right)}=\frac{2}{52}=\frac{1}{26}$

Number of black 8s $=2$

∴ ${\mathrm{P}}_{\left(\mathrm{black}8\right)}=\frac{2}{52}=\frac{1}{26}$

#### Page No 258:

#### 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)

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

(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)

∴ ${\mathrm{P}}_{\left(\mathrm{black}\mathrm{card}\right)}=\frac{26}{52}=\frac{1}{2}$

#### Page No 258:

#### 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) $\frac{5}{3}$

(b) $\frac{5}{8}$

(c) $\frac{1}{5}$

(d) $\frac{3}{8}$

#### Answer:

(b) $\frac{5}{8}$

The wheel has a total of $5+3=8$ sectors.

Number of green sectors = 5

Now, ${\mathrm{P}}_{\left(\mathrm{getting}\mathrm{a}\mathrm{green}\mathrm{sector}\right)}=\frac{5}{8}$

#### Page No 258:

#### 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) $\frac{1}{2}$

(b) $\frac{3}{4}$

(c) $\frac{3}{8}$

(d) $\frac{3}{5}$

#### Answer:

(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, ${\mathrm{P}}_{\left(\mathrm{getting}\mathrm{a}\mathrm{number}\mathrm{less}\mathrm{than}4\right)}=\frac{3}{8}$

#### Page No 258:

#### Question 3:

**Tick (✓) the correct answer:**

Two coins are tossed simultaneously. What is the probability of getting one head and one tail?

(a) $\frac{1}{4}$

(b) $\frac{1}{2}$

(c) $\frac{3}{4}$

(d) $\frac{2}{3}$

#### Answer:

(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 $=2$

$\mathrm{Now},{\mathrm{P}}_{\left(\mathrm{one}\mathrm{head}\mathrm{and}\mathrm{one}\mathrm{tail}\right)}=\frac{2}{4}=\frac{1}{2}$

#### Page No 258:

#### 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) $\frac{1}{2}$

(b) $\frac{2}{3}$

(c) $\frac{1}{5}$

(d) $\frac{2}{5}$

#### Answer:

(d) $\frac{2}{5}$

Total number of outcomes $=5$

Number of red balls $=2$

$\mathrm{Now},{\mathrm{P}}_{\left(\mathrm{red}\mathrm{ball}\right)}=\frac{2}{5}$

#### Page No 258:

#### Question 5:

**Tick (✓) the correct answer:**

A die is thrown. What is the probability of getting 6?

(a) 1

(b) $\frac{1}{6}$

(c) $\frac{6}{1}$

(d) none of these

#### Answer:

(b) $\frac{1}{6}$

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

Total number of outcomes $=6$

Now, ${\mathrm{P}}_{(\mathrm{getting}6)}=\frac{1}{6}$

#### Page No 258:

#### Question 6:

**Tick (✓) the correct answer:**

A die is thrown. What is the probability of getting an even number?

(a) $\frac{1}{2}$

(b) $\frac{2}{3}$

(c) $\frac{5}{6}$

(d) $\frac{1}{6}$

#### Answer:

(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, ${\mathrm{P}}_{\left(\mathrm{even}\mathrm{number}\right)}=\frac{3}{6}=\frac{1}{2}$

#### Page No 258:

#### 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) $\frac{1}{4}$

(b) $\frac{1}{52}$

(c) $\frac{1}{13}$

(d) $\frac{1}{26}$

#### Answer:

(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)

$\mathrm{Now},{\mathrm{P}}_{\left(\mathrm{queen}\right)}=\frac{4}{52}=\frac{1}{13}$

#### Page No 259:

#### 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) $\frac{3}{26}$

(b) $\frac{1}{26}$

(c) $\frac{1}{13}$

(d) $\frac{1}{52}$

#### Answer:

(b) $\frac{1}{26}$

Total number of cards = 52Total number of black 6 cards = 2 (6 of spades, 6 of cloves)

Now, ${\mathrm{P}}_{(\mathrm{b}\mathrm{l}\mathrm{a}\mathrm{c}\mathrm{k}6)}=\frac{2}{52}=\frac{1}{26}$

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