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A concrete beam may fail either by shear (S) or flexure (F). Suppose that three failed beams are randomly selected and the type of failure is determined for each one. Let X = the number of beams among the three selected that failed by shear. List each outcome in the sample space along with the associated value of X.
S: FFF SFF FSF FFS FSS SFS SSF SSS X:

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MrRoyal

Answer:

[tex]\begin{array}{cc}{Outcome} & {X's} & {FFF} & {0} & {SFF} & {1} & {FSF} & {1} & {FFS} & {1} & {FSS} & {2}& {SFS} & {2}& {SSF} & {2}& {SSS} & {3} \ \end{array}[/tex]

Step-by-step explanation:

Given

[tex]S_S = \{FFF, SFF, FSF, FFS, FSS, SFS, SSF, SSS\}[/tex]

[tex]X \to[/tex] Number of beams failed by shear

Required

List each outcome and the value of X

To do this, we simply count the occurrence of S in each outcome.

This is tabulated as follows:

[tex]\begin{array}{cc}{Outcome} & {X's} & {FFF} & {0} & {SFF} & {1} & {FSF} & {1} & {FFS} & {1} & {FSS} & {2}& {SFS} & {2}& {SSF} & {2}& {SSS} & {3} \ \end{array}[/tex]

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