Chapter 5.3, Problem 1.2CYU

To determine

To find: $P\left(E|L\right)$ and $P\left(L|E\right)$ . Also, identify whether the probability explains that EPS students of college are getting lower marks than those of social sciences and liberal arts.

Answer to Problem 1.2CYU

The probabilities are 0.219 and 0.50 respectively.

Explanation of Solution

Given:

The table is:

	Grade Level
School	A	B	Below B
Liberal Arts	2142	1890	2268
Engineering and Physical Sciences	368	432	800
Health and Human Services	882	630	588

Calculation:

  $P\left(E|L\right)$ and $P\left(L|E\right)$

are calculated as:

  $\begin{array}{c}P\left(E|L\right)=\frac{800}{2268+800+588}\\ =0.219\\ P\left(L|E\right)=\frac{800}{368+432+800}\\ =0.50\end{array}$

The required probabilities are 0.219 and 0.50 respectively. To reach at the conclusion it is required to make the comparison of these two computed probabilities.