Introduction to Mathematical Modelling

Question
CBSEENMA9004107

Two coins are tossed simultaneously 300 times. The frequency of appearing:

(i)  both heads : 75
(ii)  one head : 160
(iii)  No head : 65

Find the probability of occurrence of each of these events. 

Solution

Solution not provided.
Ans.  left parenthesis straight i right parenthesis space 1 fourth space space space space left parenthesis ii right parenthesis space 8 over 15 space space space left parenthesis iii right parenthesis space 13 over 60

Question
CBSEENMA9004108

Three coins are tossed simultaneously 250 times. The distribution of various outcomes is listed below:

(i)  Three tails : 30
(ii)  Both tails : 70
(iii)  One tail: 90
(iv)  No tails : 60
Find the respective probability of each event and check that the sum of all the probabalities is

Solution

Solution not provided.
Ans.  left parenthesis straight i right parenthesis space space 3 over 25 space space left parenthesis ii right parenthesis space space 7 over 25 space space left parenthesis iii right parenthesis space 9 over 25 space space left parenthesis iv right parenthesis space 6 over 25

Question
CBSEENMA9004109

The weekly pocket expenses of students are given below. Find the probability that the weekly pocket expenses of a student are:

(i) र 59
(ii)  more than र 59
(iii)  less than र 59

Pocket expenses (in र)

No. of students

45

7

40

4

59

10

71

6

58

3

63

8

65

1

Solution

Solution not provided.
Ans.  left parenthesis straight i right parenthesis space 10 over 39 space space space left parenthesis ii right parenthesis space 20 over 39 space space left parenthesis iii right parenthesis space 11 over 39

Question
CBSEENMA9004110

The percentage of marks obtained by a student in the monthly unit tests are given below:

Unit test

No. of marks obtained

I

76

II

52

III

60

IV

95

V

43

Based on this data, find the probability that the

(a)  student gets less than 60% marks in a unit test

(b)  student gets at least 60% marks in a unit test

Solution

Solution not provided.
Ans.  left parenthesis straight a right parenthesis space space space 2 over 5 space space space space space space space left parenthesis straight b right parenthesis space space space space space 3 over 5