Each test of a new type of plane can end in success S or fai

Each test of a new type of plane can end in success (S) or failure (F). Consider the outcomes of the sequential tests of three new planes. Let X represent the number of successes in the three tests. Let Y equal one if the first plane tested was successful and 0 otherwise. Consider the table of outcomes shown below.

a. What is the value of A in the table above?  

b. What is the value of B in the table above?  
c. What is the value of C in the table above?

Solution

when 3 planes are tested then the total possible cases are = 23 = 8

sample space is {SSS,SSF,SFS,SFF,FSS,FSF,FFS,FFF}

Outcome   FFF   FFS   FSF   A   FSS   SFS   SSF   SSS
X   0   1   B   1   2   2   2   3
Y   0   0   0   1   0   1   1   C
Let X represent the number of successes in the three tests.

HENCE A = SFF =1

B = 1

Let Y equal one if the first plane tested was successful and 0 otherwise

C=1