There are two preliminary reviews and one review for submitting articles to magazines. Those who pass the first trial twice can be hired; Only those who have passed the preliminary examination can enter the retrial; Those who fail the preliminary examination will not be hired. After examination, you can be hired. It is known that the probability of passing the first trial is 0.5, and the probability of passing the second trial is 0.3, and each reviewer independently reviews the manuscript.

(Question): What is the probability of delivering a manuscript through employment?

Let A stand for the event: the manuscript can pass the review of two preliminary evaluation experts;

B stands for event: the manuscript has just passed the examination of a preliminary expert;

C stands for event: the manuscript can pass the review of the review experts;

D stands for event: the manuscript was hired.

Then D=A+B*C

P(A)=0.5*0.5=0.25，P(B)=2*0.5*0.5=0.5，P(C)=0.3

P(D)=P(A+B*C)

=P(A)+P(B)*P(C)

=0.25+0.5*0.3=0.40

(2): What is the probability that at least two of the four manuscripts will be accepted?

Let A0 represent the event: 1 of the 4 manuscripts were not hired:

A 1 indicates the event: exactly 1 of the four manuscripts was hired:

A2 represents an event: at least two of the four manuscripts were hired.

p(a0)=( 1-0.4)^4=0. 1296

p(a 1)=4*0.4*( 1-0.4)^3=0.3456

P(A0+A 1)=P(A)+P(A 1)

=0. 1296+.3456=0.4752

P(A2)= 1-P(A0+a 1)= 1-0.4752 = 0.5248。