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Three professors at George Washington University did an experiment to determine if economists are more selfish than other people. They dropped $64$stamps, addressed envelopes with $\$10$cash in different classrooms on the George Washington campus. $44\%$were returned overall. From the economic classes, $56\%$of the envelopes were returned. From the business, psychology, and history classes $31\%$were returned.

Let $\text{R}=$money returned

$\text{E}=$economic classes

$\text{O}=$other classes

Given that $44\%$were returned overall.

Thus, the probability for the overall percent of money returned is given as

$P\left(R\right)=0.44$

Three professors at George Washington University did an experiment to determine if economists are more selfish than other people. They dropped $64$stamps, addressed envelopes with $\$10$cash in different classrooms on the George Washington campus. $44\%$were returned overall. From the economic classes, $56\%$ of the envelopes were returned. From the business, psychology, and history classes $31\%$ were returned.

Let $\text{R}=$money returned

$\text{E}=$economic classes

$\text{O}=$other classes

Given that from the economic classes $56\%$of the envelopes were returned.

Thus, the probability for the percent of money returned out of the economic classes is given as$P\left(R|E\right)=0.56$

Three professors at George Washington University did an experiment to determine if economists are more selfish than other people. They dropped $64$stamps, addressed envelopes with $\$10$cash in different classrooms on the George Washington campus. $44\%$were returned overall. From the economic classes, $56\%$ of the envelopes were returned. From the business, psychology, and history classes $31\%$ were returned.

Let $\text{R}=$money returned

$\text{E}=$economic classes

$\text{O}=$other classes

Given that from the other classes (business, psychology, and history classes), $31\%$were returned.

Thus, the probability for the percent of money returned out of the other classes is given as

$P\left(R|O\right)=0.31$

Three professors at George Washington University did an experiment to determine if economists are more selfish than other people. They dropped $64$stamps, addressed envelopes with $\$10$cash in different classrooms on the George Washington campus. $44\%$were returned overall. From the economic classes, $56\%$ of the envelopes were returned. From the business, psychology, and history classes $31\%$ were returned.

Let the events be

$\text{R}=$money returned

$\text{E}=$economic classes

$\text{O}=$other classes

Here, Let us first check if $P\left(R|E\right)=P\left(R\right)$

We have

$$\begin{gathered} P\left(R|E\right)=0.56 \\ P\left(R\right)=0.44 \\ P(R鈭�E)鈮�P\left(R\right) \end{gathered}$$

The first condition is not satisfied.

Therefore, the events are not independent.

Three professors at George Washington University did an experiment to determine if economists are more selfish than other people. They dropped $64$stamps, addressed envelopes with $\$10$cash in different classrooms on the George Washington campus. $44\%$were returned overall. From the economic classes, $56\%$of the envelopes were returned. From the business, psychology, and history classes $31\%$were returned.

Let the events be

$\text{R}=$money returned

$\text{E}=$economic classes

$\text{O}=$other classes

Here, Let us first check if $P\left(R|E\right)=P\left(R\right)$

We have

$$\begin{gathered} P\left(R|E\right)=0.56 \\ P\left(R\right)=0.44 \\ \text{Thus},P\left(R|E\right)>P\left(R\right) \end{gathered}$$