# In a General Social Survey of Americans in 1991, two variables, gender and finding life exciting or dull, were measured on 980 individuals. The two-wa

Burhan Hopper 2021-03-02 Answered
In a General Social Survey of Americans in 1991, two variables, gender and finding life exciting or dull, were measured on 980 individuals. The two-way table below summarizes the results.
Let A = randomly chosen person is female
Let B = randomly chosen person finds life exciting
(a) Find P(A | B)
(b) Are the events A & B independent?
$\begin{array}{ccccc}\text{Original Counts}& \text{Exciting}& \text{Routine}& \text{Dull}& \text{Total}\\ \text{Male}& 213& 200& 12& 425\\ \text{Female}& 221& 305& 29& 555\\ \text{Female}& 434& 505& 41& 980\end{array}$
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Step 1 Let A is the event that a randomly chosen person is female. Let B is the event a randomly chosen person finds life exciting. It is noted that if the two events are independent, then the conditional probability can be written as follows: $P\left(\frac{A}{B}\right)=P\left(A\right)$

Step 2

a) The conditional probability of A given B is as follows: $P\left(\frac{A}{B}\right)=P\left(A\right)$
$=\frac{555}{980}$
$\approx 0.57$

Step 3

b). Here, a randomly chosen person finds life exciting can be either male or female. There is condition on it. Thus, there is no influence of one event to other event. Hence the events A and B are independent.