A certain journal likes to give new writers an opportunity. Therefore, there is a 40% chance that an author’s first article submitted will be published. But, that author’s second article submitted, and each article submitted after that, have only a 20% chance of being published. Past history of being published has no influence on whether a new article will be published.
(a) What is the probability that a new author will be published for the first time when he or she
submits a 4th article?
(b) What is the probability a new author will be published for the first time within his or her first 5
articles submitted?

Now from the question we are told to obtain the probability that a new author will be published for the first time when he or she submits a 4th article, which implies that the new authors first three articles where not published

So the probability is mathematically represented as

[tex]P(A_4) = P(A)' * P(N)' * P(N)' * P(N)[/tex]

=> [tex]P(A_4) = 0.6 * 0.8 * 0.8* 0.2[/tex]

=> [tex]P(A_4) = 0.077[/tex]

Generally the probability that a new author will be published for the first time within his or her first 5 articles submitted is equivalent to

1 - [The probability that a new author will not be published for the first time

within his or her first 5 articles submitted]

Now the probability that a new author will not be published for the first time within his or her first 5 articles submitted. is mathematically represented as

[tex]P(A_5)' = P(A)' * P(N)' * P(N)'*P(N)'* P(N)'[/tex]

=> [tex]P(A_5)' = 0.6 *0.8 * 0.8'*0.8* 0.8[/tex]

=> [tex]P(A_5)' = 0.24576 [/tex]

Generally the probability that a new author will be published for the first time within his or her first 5 articles submitted is mathematically represented as

[tex]P(A_5) = 1 - P(A_5)'[/tex]

=> [tex]P(A_5) = 1 -0.24576 [/tex]

=> [tex]P(A_5) =0.7542 [/tex]