Question

Find $P(E|L)$ and $P(L|E)$ Which of these conditional probabilities tells you whether this college’s EPS students tend to earn lower grades than students in liberal arts and social sciences? Explain.

Short answer

The probability are $0.219$ and $0.50$

Step-by-step solution

Step 1. Given Information

The table is:

Step 2. Concept Used

Formula used: $Probability=\frac{Numberoffavorableoutcomes}{Totalpossibleoutcomes}$

Step 3. Calculation

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

are calculated as:

$P\left(E\right|L)=\frac{800}{2268+800+588}=0.219$

$P\left(F\right|L)=\frac{800}{368+432+800}=0.50$

The probabilities necessary are $0.219$and $0.50$, respectively. It is necessary to compare these two estimated probabilities in order to arrive at a conclusion.