Data Handling IV (Probability) RD Sharma Solutions | Mathematics (Maths) Class 7 PDF Download

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1. A coin is tossed 1000 times with the following frequencies: 
Head: 445, Tail: 555 
When a coin is tossed at random, what is the probability of getting? 
(i) A head? 
(ii) A tail? 
 
Solution: 
Given 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 head = number of heads/total number of trails 
= (445/1000) 
= 0.445 
 
(ii) Probability of getting tail = number of tail/total number of trails 
= (555/1000) 
= 0.555 
 
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 
If a die is thrown at random, find the probability of getting a/an: 
(i) 3  
(ii) 5  
(iii) 4  
(iv) Even number  
(v) Odd number  
(vi) Number less than 3. 
 
Solution: 
Given total number of trials = 100 
(i) From the table, number of times 3 comes up = 14 
Probability of getting 3 = frequency of 3/ total number of trails 
= 14/100 
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1. A coin is tossed 1000 times with the following frequencies: 
Head: 445, Tail: 555 
When a coin is tossed at random, what is the probability of getting? 
(i) A head? 
(ii) A tail? 
 
Solution: 
Given 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 head = number of heads/total number of trails 
= (445/1000) 
= 0.445 
 
(ii) Probability of getting tail = number of tail/total number of trails 
= (555/1000) 
= 0.555 
 
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 
If a die is thrown at random, find the probability of getting a/an: 
(i) 3  
(ii) 5  
(iii) 4  
(iv) Even number  
(v) Odd number  
(vi) Number less than 3. 
 
Solution: 
Given total number of trials = 100 
(i) From the table, number of times 3 comes up = 14 
Probability of getting 3 = frequency of 3/ total number of trails 
= 14/100 
 
 
 
 
 
   
 
= 7/50 
 
(ii) From the table, number of times 5 comes up = 18 
Probability of getting 5 = frequency of 5/ total number of trails 
= 18/100 
= 9/50 
 
(iii) From the table, number of times 4 comes up = 23 
Probability of getting 4 = frequency of 4/ total number of trails 
= 23/100 
 
(iv) Frequency of getting an even number = Frequency of 2 + Frequency of 4 + Frequency 
of 6  
= 9 + 23 + 15  
= 47 
Probability of getting an even number = frequency of an even number/ total number of 
trails 
= 47/100 
 
(v) Frequency of getting an even number = Frequency of 1 + Frequency of 3 + Frequency 
of 5 
= 21 + 14 + 18 
= 53 
Probability of getting odd number = frequency of odd number/ total number of trails 
= 53/100 
 
(vi) Frequency of getting number less than 3 = Frequency of 1 + Frequency of 2 
= 21 + 9 
= 30 
Probability of getting number less than 3 = frequency of number less than 3/ total 
number of trails 
= 30/100 
= 3/10 
 
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? 
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1. A coin is tossed 1000 times with the following frequencies: 
Head: 445, Tail: 555 
When a coin is tossed at random, what is the probability of getting? 
(i) A head? 
(ii) A tail? 
 
Solution: 
Given 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 head = number of heads/total number of trails 
= (445/1000) 
= 0.445 
 
(ii) Probability of getting tail = number of tail/total number of trails 
= (555/1000) 
= 0.555 
 
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 
If a die is thrown at random, find the probability of getting a/an: 
(i) 3  
(ii) 5  
(iii) 4  
(iv) Even number  
(v) Odd number  
(vi) Number less than 3. 
 
Solution: 
Given total number of trials = 100 
(i) From the table, number of times 3 comes up = 14 
Probability of getting 3 = frequency of 3/ total number of trails 
= 14/100 
 
 
 
 
 
   
 
= 7/50 
 
(ii) From the table, number of times 5 comes up = 18 
Probability of getting 5 = frequency of 5/ total number of trails 
= 18/100 
= 9/50 
 
(iii) From the table, number of times 4 comes up = 23 
Probability of getting 4 = frequency of 4/ total number of trails 
= 23/100 
 
(iv) Frequency of getting an even number = Frequency of 2 + Frequency of 4 + Frequency 
of 6  
= 9 + 23 + 15  
= 47 
Probability of getting an even number = frequency of an even number/ total number of 
trails 
= 47/100 
 
(v) Frequency of getting an even number = Frequency of 1 + Frequency of 3 + Frequency 
of 5 
= 21 + 14 + 18 
= 53 
Probability of getting odd number = frequency of odd number/ total number of trails 
= 53/100 
 
(vi) Frequency of getting number less than 3 = Frequency of 1 + Frequency of 2 
= 21 + 9 
= 30 
Probability of getting number less than 3 = frequency of number less than 3/ total 
number of trails 
= 30/100 
= 3/10 
 
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? 
 
 
 
 
 
   
 
 
Solution: 
Given number 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 
Number of white socks left = 2 – 1 = 1 
Probability of getting white socks = number of white socks left in the box/ total number 
of socks left in the box 
= 1/3 
 
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 
If same pair of coins is tossed at random, find the probability of getting: 
(i) Two heads  
(ii) One head  
(iii) No head. 
 
Solution: 
Given number of trials = 500 
From the given table it is clear that, 
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 = frequency of getting 2 heads/ total number of trials 
= 105/500 
= 21/100 
 
(ii) Probability of getting one head = frequency of getting 1 heads/ total number of trials 
= 275/500 
= 11/20 
 
(iii) Probability of getting no head = frequency of getting no heads/ total number of trials 
= 120/500 
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1. A coin is tossed 1000 times with the following frequencies: 
Head: 445, Tail: 555 
When a coin is tossed at random, what is the probability of getting? 
(i) A head? 
(ii) A tail? 
 
Solution: 
Given 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 head = number of heads/total number of trails 
= (445/1000) 
= 0.445 
 
(ii) Probability of getting tail = number of tail/total number of trails 
= (555/1000) 
= 0.555 
 
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 
If a die is thrown at random, find the probability of getting a/an: 
(i) 3  
(ii) 5  
(iii) 4  
(iv) Even number  
(v) Odd number  
(vi) Number less than 3. 
 
Solution: 
Given total number of trials = 100 
(i) From the table, number of times 3 comes up = 14 
Probability of getting 3 = frequency of 3/ total number of trails 
= 14/100 
 
 
 
 
 
   
 
= 7/50 
 
(ii) From the table, number of times 5 comes up = 18 
Probability of getting 5 = frequency of 5/ total number of trails 
= 18/100 
= 9/50 
 
(iii) From the table, number of times 4 comes up = 23 
Probability of getting 4 = frequency of 4/ total number of trails 
= 23/100 
 
(iv) Frequency of getting an even number = Frequency of 2 + Frequency of 4 + Frequency 
of 6  
= 9 + 23 + 15  
= 47 
Probability of getting an even number = frequency of an even number/ total number of 
trails 
= 47/100 
 
(v) Frequency of getting an even number = Frequency of 1 + Frequency of 3 + Frequency 
of 5 
= 21 + 14 + 18 
= 53 
Probability of getting odd number = frequency of odd number/ total number of trails 
= 53/100 
 
(vi) Frequency of getting number less than 3 = Frequency of 1 + Frequency of 2 
= 21 + 9 
= 30 
Probability of getting number less than 3 = frequency of number less than 3/ total 
number of trails 
= 30/100 
= 3/10 
 
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? 
 
 
 
 
 
   
 
 
Solution: 
Given number 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 
Number of white socks left = 2 – 1 = 1 
Probability of getting white socks = number of white socks left in the box/ total number 
of socks left in the box 
= 1/3 
 
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 
If same pair of coins is tossed at random, find the probability of getting: 
(i) Two heads  
(ii) One head  
(iii) No head. 
 
Solution: 
Given number of trials = 500 
From the given table it is clear that, 
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 = frequency of getting 2 heads/ total number of trials 
= 105/500 
= 21/100 
 
(ii) Probability of getting one head = frequency of getting 1 heads/ total number of trials 
= 275/500 
= 11/20 
 
(iii) Probability of getting no head = frequency of getting no heads/ total number of trials 
= 120/500 
 
 
 
 
 
   
 
= 6/25