RD Sharma Solutions for Class 7 Maths Chapter 25 Data Handling - IV (Probability) Free Online
Ex 25.1 Page No.: 25.6
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
