A survey of 1,700 shoppers asked, "Does social media influence your purchase decisions?" The results indicated that 20.3% of females responded that their purchase decisions are influenced by social media compared to 10.5% of males. (Data extracted from "The myth of the mansumer...," bit.ly/1JVaKoh.) The sample sizes of males and females were not provided. Suppose that the results indicated that of 850 males, 89 answered yes. Of 850 females, 173 answered yes.
a. Suppose that the respondent chosen is a female. What is the probability that her purchase decisions are influenced by social media?
b. Suppose that the respondent chosen does indicate that his/her purchase decisions are influenced by social media. What is the probability that the individual is a male?
c. Are influence of purchase decisions by social media and the gender of the individual independent? Explain.