Extra points: Problem

In this time for this entry, will solve the problem 1.5.2 of the book Introduction to Information Theory and Data Compression.

The problem here:

2. In eight tosses of a fair coin, find the probability that heads will come up
(a) exactly three times;
(b) at least three times;
(c) at most three times.

Answers:

A)
To solve this part i used next formula:

Where:

• "k" is the number of hits.
• "n" is the number of trials.
• "p" is the probability of success

now resolve:

and the result is: 0.875


B)
To solve this part i used next formula

Where:

• "k" is the number of hits.
• "n" is the number of trials.
• "p" is the probability of succes
• "u" is the exactly k succes (sigma)

now resolve:

=

=

and the result is: 2.2226

C)
To resolve this part i used the next formula:

 Where:

• P is probability of the event,
• C (n, k) are combinations of k elements from n elements a total
• p is the probability of success and q = (1-p) the probability of failure
• n number of times to repeat the individual case
• k number of successes

now resolve:

and the result is:1/256