Homework Sourse1 Each test of a new type of plane can end in success S or f
1) 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?
Can you explain how to get these as well?
| Outcome | FFF | FFS | FSF | SFF | FSS | A | SSF | SSS |
| X | 0 | 1 | 1 | 1 | 2 | 2 | B | 3 |
| Y | 0 | 0 | 0 | C | 0 | 1 | 1 | 1 |
Solution
a. When 3 planes are tested for each with two possible outcomes success(S) or failure (F), all possible combinations are:
(FFF) (FFS) (FSF) (SFF) (FSS) (SFS) (SSF) (SSS)
All possible outcomes are listed above except (SFS)
Thus, value of A is (SFS)
b. X represents the number of successes in the outcome.
Number of successes in the outcome (SSF) is 2.
Thus, value of B = 2.
c. Y represents 1 if first plane was tested successful otherwise zero. i.e. Y is 1 is combination of outcome start with S otherwise 0.
First outcome of the string SFF is S (i.e. success) thus corresponding Y value is 1.
Thus, C = 1
