Independent solution

How to solve this Inclusion–Exclusion question

Setup

Setup

Complete the high, normal, and low column marginals first; the normal column has probability 1-0.14-0.22=0.64.

Pr⁡(N)=1−0.14−0.22=0.64\Pr(N)=1-0.14-0.22=0.64

Model

Model

Use the supplied fractions within the irregular row to obtain its high and normal cells, then subtract those cells from the irregular marginal.

Pr⁡(I∩H)=0.15/3=0.05\Pr(I\cap H)=0.15/3=0.05
Pr⁡(I∩N)=0.64/8=0.08\Pr(I\cap N)=0.64/8=0.08

Compute

Compute

The irregular-low cell is 0.15-0.05-0.08=0.02. Removing it from the low marginal 0.22 leaves 0.20 in the regular-low cell.

Pr⁡(I∩L)=0.15−0.05−0.08=0.02\Pr(I\cap L)=0.15-0.05-0.08=0.02
Pr⁡(Ic∩L)=0.22−0.02=0.20\Pr(I^c\cap L)=0.22-0.02=0.20

Answer

Answer

The requested regular-and-low probability is 20%, corresponding to choice E.

20%(E)\boxed{20\%\quad\text{(E)}}