In a survey of 302 people, the following data were obtained relating gender to political orientation:

Republican (R) Democrat (D) Independent (I) Total
Male (M) 85 43 37 165
Femal (F) 43 79 15 137
Total 128 122 52 302

What is the probability that the person is republican given that the person is male?

To find the probability that a person is Republican given that the person is male, we need to use conditional probability.

Conditional probability is defined as the probability of an event occurring given that another event has already occurred. In this case, we want to find the probability of a person being Republican (R) given that the person is male (M).

We can use the formula for conditional probability: P(A|B) = P(A and B) / P(B)

Here, A represents the event of being Republican (R), and B represents the event of being male (M).

To find P(A and B), we look at the table you provided. According to the table, there are 85 males who are Republican (R). Therefore, P(A and B) = 85 / 302.

To find P(B), we need to calculate the total number of males from the table. According to the table, there are 165 males. Therefore, P(B) = 165 / 302.

Now, we can calculate the probability using the formula:

P(A|B) = P(A and B) / P(B) = (85 / 302) / (165 / 302) = 85 / 165.

So, the probability that the person is Republican given that the person is male is 85/165 or approximately 0.5152 (rounded to four decimal places).