## 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