Question :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 obtaining?
(i) A head?
(ii) A tail?
Solution 1:
Specified below that total number of times a coin is tossed = 1000
Head comes in coin = 445
Tail comes in a coin = 555
(i) Probability of obtaining head = ((number of heads)/(total number of trails))
= (445/100) = 0.445
(ii) Probability of obtaining tail = ((number of tail)/(total number of trails))
= ((.555)/1000) = 0.555
Question :2. A die is thrown 100 times and outcomes are noted as Specified below that below:
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)