Rd Sharma 2018 Solutions for Class 7 Math Chapter 1 Integers are provided here with simple step-by-step explanations. These solutions for Integers are extremely popular among Class 7 students for Math Integers Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Rd Sharma 2018 Book of Class 7 Math Chapter 1 are provided here for you for free. You will also love the ad-free experience on Meritnationâ€™s Rd Sharma 2018 Solutions. All Rd Sharma 2018 Solutions for class Class 7 Math are prepared by experts and are 100% accurate.

#### Page No 25.6:

#### Question 1:

A coin is tossed 1000 times with the following frequencies:

Head: 445, | Tail: 555 |

#### Answer:

Total number of times a coin is tossed = 1000

Number of times a head comes up = 445

Number of times a tail comes up = 555

(i) Probability of getting a head = $\frac{\mathrm{Number}\mathrm{of}\mathrm{heads}}{\mathrm{Total}\mathrm{no}.\mathrm{of}\mathrm{trails}}=\frac{445}{1000}=0.445$

(ii) Probability of getting a tail = $\frac{\mathrm{Number}\mathrm{of}\mathrm{tails}}{\mathrm{Total}\mathrm{no}.\mathrm{of}\mathrm{trails}}=\frac{555}{1000}=0.555$

#### Page No 25.6:

#### Question 2:

A die is thrown 100 times and outcomes are noted as given below:

Outcome: | 1 | 2 | 3 | 4 | 5 | 6 |

Frequency: | 21 | 9 | 14 | 23 | 18 | 15 |

*a*/

*an*.

(i) 3

(ii) 5

(iii) 4

(iv) Even number

(v) Odd number

(vi) Number less than 3.

#### Answer:

Total number of trials = 100

Number of times "1" comes up = 21

Number of times "2" comes up = 9

Number of times "3" comes up = 14

Number of times "4" comes up = 23

Number of times "5" comes up = 18

Number of times "6" comes up = 15

(i) Probability of getting 3

=$\frac{\mathrm{frequency}\mathrm{of}3}{\mathrm{Total}\mathrm{no}.\mathrm{of}\mathrm{trails}}=\frac{14}{100}=0.14$

(ii) Probability of getting 5

= $\frac{\mathrm{frequency}\mathrm{of}5}{\mathrm{Total}\mathrm{no}.\mathrm{of}\mathrm{trails}}=\frac{18}{100}=0.18$

(iii) Probability of getting 4

=$\frac{\mathrm{frequency}\mathrm{of}4}{\mathrm{Total}\mathrm{no}.\mathrm{of}\mathrm{trails}}=\frac{23}{100}=0.23$

(iv) Frequency of getting an even no. = Frequency of 2 + Frequency of 4 + Frequency of 6 = 9+ 23 + 15 = 47

Probability of getting an even no. =$\frac{\mathrm{frequency}\mathrm{of}\mathrm{even}\mathrm{no}.}{\mathrm{Total}\mathrm{no}.\mathrm{of}\mathrm{trails}}=\frac{47}{100}=0.47$

(v) Frequency of getting an odd no. = Frequency of 1 + Frequency of 3 + Frequency of 5 = 21+ 14 + 18 = 53

Probability of getting an odd no. =$\frac{\mathrm{frequency}\mathrm{of}\mathrm{odd}\mathrm{no}.}{\mathrm{Total}\mathrm{no}.\mathrm{of}\mathrm{trails}}=\frac{53}{100}=0.53$

(vi) Frequency of getting a no. less than 3 = Frequency of 1 + Frequency of 2= 21 + 9 = 30

Probability of getting a no. less than 3

=$\frac{\mathrm{frequency}\mathrm{of}\mathrm{no}.\mathrm{less}\mathrm{than}3}{\mathrm{Total}\mathrm{no}.\mathrm{of}\mathrm{trails}}=\frac{30}{100}=0.30$

#### Page No 25.6:

#### Question 3:

A box contains two pair of socks of two colours (black and white). I have picked out a white sock. I pick out one more with my eyes closed. What is the probability that I will make a pair?

#### Answer:

No. of socks in the box = 4

Let B and W denote black and white socks respectively.

Then we have:

S = {B,B,W,W}

If a white sock is picked out, then the total no. of socks left in the box = 3

No. of white socks left = 2-1 =1

Probability of getting a white sock

=$\frac{\mathrm{Number}\mathrm{of}\mathrm{white}\mathrm{socks}\mathrm{left}\mathrm{in}\mathrm{the}\mathrm{box}}{\mathrm{Total}\mathrm{no}.\mathrm{of}\mathrm{socks}\mathrm{left}\mathrm{in}\mathrm{the}\mathrm{box}}=\frac{1}{3}$

#### Page No 25.6:

#### Question 4:

Two coins are tossed simultaneously 500 times and the outcomes are noted as given below:

Outcome: | Two heads (HH) |
One head (HT or TH) |
No head (TT) |

Frequency: | 105 | 275 | 120 |

#### Answer:

Number of trials = 500

Number of outcomes of two heads (HH) = 105

Number of outcomes of one head (HT or TH) = 275

Number of outcomes of no head (TT) = 120

(i) Probability of getting two heads =$\frac{\mathrm{frequency}\mathrm{of}\mathrm{getting}2\mathrm{heads}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{trails}}=\frac{105}{500}=\frac{21}{100}$

(ii) Probability of getting one head =$\frac{\mathrm{frequency}\mathrm{of}\mathrm{getting}1\mathrm{head}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{trails}}=\frac{255}{500}=\frac{11}{20}$

(iii) Probability of getting no head =$\frac{\mathrm{frequency}\mathrm{of}\mathrm{getting}\mathrm{no}\mathrm{head}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{trails}}=\frac{120}{500}=\frac{6}{25}$

#### Page No 25.7:

#### Question 1:

An unbiased coin is tossed once, the probability of getting head is

(a) $\frac{1}{2}$ (b) 1 (c) $\frac{1}{3}$ (d) $\frac{1}{4}$

#### Answer:

Tossing a coin, either we get a head (H) or a tail (T). So, the probability of getting a head is $\frac{1}{2}$.

Hence, the correct option is (a).

#### Page No 25.7:

#### Question 2:

There are 10 cards numbered from 1 to 10. A card is drawn randomly. The probability of getting

an even numbered card is

(a) $\frac{1}{10}$ (b) $\frac{1}{5}$ (c) $\frac{1}{2}$ (d) $\frac{2}{5}$

#### Answer:

The number on the cards are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

The even numbers on the cards are 2, 4, 6, 8, 10.

∴ Probability of getting an even numbered card = $\frac{\mathrm{Number}\mathrm{of}\mathrm{even}\mathrm{numbered}\mathrm{card}}{\mathrm{Number}\mathrm{of}\mathrm{cards}\mathrm{with}\mathrm{numbers}\mathrm{from}1\mathrm{to}10}$

$=\frac{5}{10}=\frac{1}{2}$

Hence, the correct option is (c).

#### Page No 25.7:

#### Question 3:

A dice is rolled. The probability of getting an even prime is

(a) $\frac{1}{6}$ (b) $\frac{1}{3}$ (c) $\frac{1}{2}$ (d) $\frac{5}{6}$

#### Answer:

The possible numbers on a dice are 1, 2, 3, 4, 5, 6.

There is only one even prime number which is 2.

∴ Probability of getting an even prime = $\frac{\mathrm{Number}\mathrm{of}\mathrm{even}\mathrm{prime}\mathrm{numbers}}{\mathrm{Number}\mathrm{of}\mathrm{all}\mathrm{possible}\mathrm{outcomes}\mathrm{on}\mathrm{the}\mathrm{dice}}$$=\frac{1}{6}$

Hence, the correct option is (a).

#### Page No 25.7:

#### Question 4:

There are 100 cards numbered from 1 to 100 in a box. If a card is drawn from the box and

the probability of an event is $\frac{1}{2}$, then the number of favourable cases to the event is

(a) 20 (b) 25 (c) 40 (d) 50

#### Answer:

Here, $\frac{50}{100}=\frac{1}{2}$.

So, if the the probability of an event is $\frac{1}{2}$, then the number of favourable cases has to be 50.

Hence, the correct option is (d).

#### Page No 25.7:

#### Question 5:

When a dice is thrown, the total number of possible outcomes is

(a) 6 (b) 1 (c) 3 (d) 4

#### Answer:

The number on the faces of a dice are 1, 2, 3, 4, 5, and 6.

∴ Number of possible outcomes = 6

Hence, the correct option is (a).

#### Page No 25.7:

#### Question 6:

There are 10 marbles in a box which are marked with the distinct numbers from 1 to 10.

A marble is drawn randomly. The probability of getting prime numbered marble is

(a) $\frac{1}{2}$ (b) $\frac{2}{5}$ (c) $\frac{9}{3}$ (d) $\frac{3}{10}$

#### Answer:

The numbers marked on the marbles are 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10.

Here, the prime numbers (favourable outcomes) are 2, 3, 5, and 7.

∴ Number of favourable outcomes = 4

Therefore

Probability of getting prime numbered marble = $\frac{4}{10}=\frac{2}{5}$

Hence, the correct option is (b).

#### Page No 25.7:

#### Question 7:

The probability of getting a red card from a well shuffled pack of cards is

(a) $\frac{1}{4}$ (b) $\frac{1}{2}$ (c) $\frac{3}{4}$ (d) $\frac{1}{3}$

#### Answer:

There are 52 cards in a standard deck. There are four different suits Diamonds (red), Clubs (black)

, Hearts (red), and Spades (black) each containing 13 cards.

∴ Number of red cards (favourable outcomes) = 13 + 13 = 26

Therefore

Probability of getting a red card = $\frac{26}{52}=\frac{1}{2}$

Hence, the correct option is (b).

#### Page No 25.7:

#### Question 8:

A coin is tossed 100 times and head is obtained 59 times. The probability of getting a tail is

(a) $\frac{59}{100}$ (b) $\frac{41}{100}$ (c) $\frac{29}{100}$ (d) $\frac{43}{100}$

#### Answer:

Number of all possible outcomes = 100

Number of head obtained = 59

Number of tail obtained (favourable outcomes) = 100 − 59 = 41

Therefore

Probability of getting a tail = $\frac{41}{100}$

Hence, the correct option is (b).

#### Page No 25.7:

#### Question 9:

A dice is tossed 80 times and number 5 is obtained 14 times. The probability of not getting the number 5 is

(a) $\frac{7}{40}$ (b) $\frac{7}{80}$ (c) $\frac{33}{40}$ (d) None of these

#### Answer:

Probability of getting 5 = $\frac{14}{80}=\frac{7}{40}$

Therefore

Probability of not getting 5 = $1-\frac{7}{40}=\frac{33}{40}$

Hence, the correct option is (c).

#### Page No 25.7:

#### Question 10:

A bag contains 4 green balls, 4 red balls and 2 blue balls. If a ball is drawn from the bag, the

probability of getting neither green nor red ball is

(a) $\frac{2}{5}$ (b) $\frac{1}{2}$ (c) $\frac{4}{5}$ (d) $\frac{1}{5}$

#### Answer:

The probability of getting neither green nor red ball is equal to the probability of getting blue balls.

Number of blue balls = 2

Total number of balls = 4 + 4 + 2 = 10

Therefore

Probability of getting neither green nor red ball = $\frac{2}{10}=\frac{1}{5}$

Hence, the correct option is (d).

View NCERT Solutions for all chapters of Class 7