**If a die is thrown at random, find the probability of obtaining a/an:**

**(i) 3**

**(ii) 5**

**(iii) 4**

**(iv) Even number**

**(v) Odd number**

**(vi) Number less than 3.**

**Solution 2:**

Specified below that total number of trials = 100

(i) From the table, no. of times 3 obtain = 14

Probability of obtaining 3 = ((frequency of 3)/(total number of trails))

= (14/100) = (7/50)

(ii) From the table, no. of times 5 occur = 18

Probability of obtaining 5 = ((frequency of 5)/(total number of trails))

= (18/100) = (5/50)

(iii) From the table, no. of times 4 occur = 23

Probability of obtaining 4 = ((frequency of 4)/(total number of trails))

= (23/100)

(iv) Frequency of obtaining an even number

= Frequency of 2 + Frequency of 4 + Frequency of 6

= 9 + 23 + 15

= 47

An even number’s obtaining probability = ((frequency of an even number)/(total number of trails))

= (47/100)

(v) Frequency of obtaining an even number

= Frequency of 1 + Frequency of 3 + Frequency of 5

= 21 + 14 + 18

= 53

An odd number’s obtaining probability = ((frequency of an odd number)/(total number of trails))

= (53/100)

(vi) Frequency of obtaining number less than 3

= Frequency of 1 + Frequency of 2

= 21 + 9

= 30

Probability of obtaining number less than 3 = ((frequency of number less than 3)/(total number of trails))

= (30/100)

= (3/10)

**Question :3. A box contains two pair of socks of two colures (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 3:**

Specified below that number of socks in the box = 4

Let B denote black and W denote white socks. Then

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 obtaining white socks = ((number of white socks left in the box)/(total number of socks left in the box))

= (1/3)

**Question :4. Two coins are tossed simultaneously 500 times and the outcomes are noted as Specified below that below:**

**If same pair of coins is tossed at random, find the probability of obtaining:**

**(i) Two heads**

**(ii) One head**

**(iii) No head. **

**Solution 4:**

Specified below that number of trials = 500

From the Specified below that 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 obtaining two heads = ((frequency of obtaining 2 heads)/(total number of trials))

= (105/500) = (21/100)

(ii) Probability of obtaining one head = ((frequency of obtaining 1 heads)/(total number of trials))

= (275/500) = (11/20)

(iii) Probability of obtaining no head = ((frequency of obtaining no heads)/(total number of trials))

= (120/500) = (6/25)