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

Burhan Hopper

Answered question

2021-03-02

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?
Original CountsExcitingRoutineDullTotalMale21320012425Female22130529555Female43450541980

Answer & Explanation

hosentak

hosentak

Skilled2021-03-03Added 100 answers

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(AB)=P(A)

Step 2

a) The conditional probability of A given B is as follows: P(AB)=P(A)
=555980
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.

Do you have a similar question?

Recalculate according to your conditions!

New Questions in High school statistics

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?