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?
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:
a) The conditional probability of A given B is as follows:
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.
A group of children and adults were polled about whether they watch a particular TV show. The survey results, showing the joint relative frequencies and marginal relative frequencies, are shown in the two-way table.
What is the value of x?
Bayes' Theorem is given by