Solving Real Analysis Problems
Real analysis is a practice where raw record is arranging and organizing such that useful information will be extracting from it. The process of organizing about numbers and to understand what the data does and does not contain. Analysis classified into qualitative and quantitative. Qualitative analysis is involved in interpreting information which can be collected during the course of qualitative research. Quantitative analysis is involved in presenting and interpreting numerical numbers.I like to share this Anova Analysis with you all through my article.
Solving Real Analysis – Solving Example Problems
Solved real analysis example problems
Example 1: A pair of balanced dice is rolled, and what are the probabilities of getting the sum (1) 7 (2) 7 or 8 (3) 9
Solution:-
The sample space S = {(1, 1), (1, 2) … (6, 6)}
Number of possible outcomes n(S) = 36
Let A be the event of getting sum 7.
Let B be the event of getting the sum 8.
Let C be the event of getting the sum 9.
A = {(1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)}, n(A) = 6.
B = {(2, 6), (3, 5), (4, 4), (5, 3), (6, 2)}, n (B) = 5
C = {(3, 6), (4, 5), (5, 4), (6, 3)}, n(C) = 4
(1) P (getting sum 7) = P(A) = n(A) / n(S)
= 6/36 = 1/6
Therefore P(7) = 1/6
(2) P (7 or 8) = P(A or B)
= P (A) + P (B) (A and B are mutually exclusive i.e. AnB=f)
= 6/36 + 5/36
= 11/36
Therefore P (7 or 8) = 11/36
(3) P (getting sum 8) = P(c) = n(A) / n(S)
= 4/36 = 1/9
Therefore P (8) = 1/9.
Example 2: Find the sum of all integers, from 10 to 1000 inclusive, which are divisible by 10.
Solution:
Sequence of first few elements of integers divisible by 10 are given by 10, 20, 30, 40...
The above sequence has a first element equal to 10 and a common difference d = 10.
We need to know the rank of the term 1000.
We use the following formula for the nth term
an = a1 + (n - 1 )d
1000 = a 1 + (n - 1 )d
Substitute a1 and d by their values
1000 = 10 + 10(n - 1)
Solve for n to obtain
n = 100
1000 is the 100th term, we can use the following formula to find sum
sn = n (a1 + an) / 2
s100 = 100 (10 + 1000) / 2 = 50500.
Between, if you have problem on these topics adding subtracting multiplying and dividing rational expressions, please browse expert math related websites for more help on tutoring math online.
Solving Real Analysis – Solving Practice Problems
Solve these practice real analysis problems
Problem 1: When a pair of balanced dice is rolled, and what are the probabilities of getting the sum (1) 12 (2) 2 (3) 6 or 7.
Answer: 1) 1/36, 2) 1/36, 3) 11/36
Problem 2: Find the sum of all integers, from 11 to 1100 inclusive, which are divisible by 11.
Answer: 61105
Real analysis is a practice where raw record is arranging and organizing such that useful information will be extracting from it. The process of organizing about numbers and to understand what the data does and does not contain. Analysis classified into qualitative and quantitative. Qualitative analysis is involved in interpreting information which can be collected during the course of qualitative research. Quantitative analysis is involved in presenting and interpreting numerical numbers.I like to share this Anova Analysis with you all through my article.
Solving Real Analysis – Solving Example Problems
Solved real analysis example problems
Example 1: A pair of balanced dice is rolled, and what are the probabilities of getting the sum (1) 7 (2) 7 or 8 (3) 9
Solution:-
The sample space S = {(1, 1), (1, 2) … (6, 6)}
Number of possible outcomes n(S) = 36
Let A be the event of getting sum 7.
Let B be the event of getting the sum 8.
Let C be the event of getting the sum 9.
A = {(1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)}, n(A) = 6.
B = {(2, 6), (3, 5), (4, 4), (5, 3), (6, 2)}, n (B) = 5
C = {(3, 6), (4, 5), (5, 4), (6, 3)}, n(C) = 4
(1) P (getting sum 7) = P(A) = n(A) / n(S)
= 6/36 = 1/6
Therefore P(7) = 1/6
(2) P (7 or 8) = P(A or B)
= P (A) + P (B) (A and B are mutually exclusive i.e. AnB=f)
= 6/36 + 5/36
= 11/36
Therefore P (7 or 8) = 11/36
(3) P (getting sum 8) = P(c) = n(A) / n(S)
= 4/36 = 1/9
Therefore P (8) = 1/9.
Example 2: Find the sum of all integers, from 10 to 1000 inclusive, which are divisible by 10.
Solution:
Sequence of first few elements of integers divisible by 10 are given by 10, 20, 30, 40...
The above sequence has a first element equal to 10 and a common difference d = 10.
We need to know the rank of the term 1000.
We use the following formula for the nth term
an = a1 + (n - 1 )d
1000 = a 1 + (n - 1 )d
Substitute a1 and d by their values
1000 = 10 + 10(n - 1)
Solve for n to obtain
n = 100
1000 is the 100th term, we can use the following formula to find sum
sn = n (a1 + an) / 2
s100 = 100 (10 + 1000) / 2 = 50500.
Between, if you have problem on these topics adding subtracting multiplying and dividing rational expressions, please browse expert math related websites for more help on tutoring math online.
Solving Real Analysis – Solving Practice Problems
Solve these practice real analysis problems
Problem 1: When a pair of balanced dice is rolled, and what are the probabilities of getting the sum (1) 12 (2) 2 (3) 6 or 7.
Answer: 1) 1/36, 2) 1/36, 3) 11/36
Problem 2: Find the sum of all integers, from 11 to 1100 inclusive, which are divisible by 11.
Answer: 61105
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