Extra Points. Excercise 1.5.1

In this post I will solve the problem 1.5.1 of the book Introduction to Information Theory and Data Compression.

This is the problem:

1. An urn contains five red, seven green, and three yellow balls. Nine are drawn, with replacement. Find the probability that

(a) exactly six of the balls drawn are green;
(b) at least two of the balls drawn are yellow;
(c) at most four of the balls drawn are red.

This is how I solve it:

For the first subsection I used this formula:

In this formula:

• "n" is the number of attempts
• "k" is the number of successes
• "p" is the probability of successes

Substitution and answer:

Now for the second subsection the formula that I used was this:

Where:

• "p" is the probability of successes
• "k" is the number of successes
• "n" is the number of attempts
• "u" is k success

Substitution and answer

And for the last subsection this is the formula:

Where:

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

Substitution and answer