Question

An outbreak of Chicken Pox hit the local public schools. Approximately $15\%$ of the male and female juniors and $25\%$ of the male and female seniors are currently healthy, $35\%$ of the male and female juniors and $30\%$ of the male and female seniors are currently sick, and $50\%$ of the male and female juniors and $45\%$ of the male and female seniors are carriers of Chicken Pox.
There are $100$ male juniors, $80$ male seniors, $120$ female juniors, and $100$ female seniors.
Using two matrices and one matrix equation, find out how many males and how many females are healthy, sick and carriers.

• A. $59$ healthy males, $35$ sick males, and $43$ carrier males, $86$ healthy females, $95$ sick females, and $72$ carrier females
• B. $35$ healthy males, $59$ sick males, and $86$ carrier males, $43$ healthy females, $72$ sick females, and $95$ carrier females
• C. $50$ healthy males, $45$ sick males, and $40$ carrier males, $87$ healthy females, $74$ sick females, and $86$ carrier females
• D. $46$ healthy males, $51$ sick males, and $37$ carrier males, $73$ healthy females, $72$ sick females, and $90$ carrier females

Answer 1

The correct option is B $35$ healthy males, $59$ sick males, and $86$ carrier males, $43$ healthy females, $72$ sick females, and $95$ carrier females

$\begin{array}{c}M\\ F\end{array}\left[\begin{array}{cc}100& 80\\ 120& 100\end{array}\right]\times \begin{array}{c}Jr\\ S_r\end{array}\left[\begin{array}{ccc}0.15& 0.35& 0.60\\ 0.25& 0.30& 0.45\end{array}\right]$

First column=Jr and second column=Sr of First matrix

First column=H, Second column=S, third column=C of second matrix

$=\left[\begin{array}{ccc}35& 59& 86\\ 43& 72& 105\end{array}\right]\begin{array}{c}Male\\ Female\end{array}$

Option B