Help And please explain Suppose an online business organizes

Help. And please explain.

Suppose an online business organizes an e-mail survey to find out if online shoppers are concerned with the security of business transactions on the Web. Of the 43 individuals who respond, 25 are concerned, and 18 are not concerned. Seven of those concerned about security are male and 6 of those not concerned are male. If a respondent is selected at random, find each of the following conditional probabilities: a) The respondent is male, given that the respondent is not concerned about security. b) The respondent is not concerned about security, given that it is female. c) The respondent is female, given that the respondent is concerned about security. a) The probability that the respondent is male, given that the respondent is not concerned about security is . (Round to three decimal places as needed.) b) The probability that the respondent is not concerned about security, given that it is female is . (Round to three decimal places as needed.) c) The probability that the respondent is female, given that the respondent is concerned about security is . (Round to three decimal places as needed.)

Solution

a) No of individuals who are not concerned = 19

No of males among individuals not concerned = 7

probability that the respondent is male, given that the respondent is not concerned about security

                              = 7/19 = 0.3684

b) No of individuals who are concerned = 25

No of females concerned = 25 - 9 = 16

No of individuals who are not concerned = 19

No of females not concerned = 16 - 7 = 9

Total females = 16 + 9 = 25

probability that the respondent is not concerned about security, given that it is female = 9/25 = 0.36

c) No of individuals who are concerned = 25

  No of females concerned = 25 - 9 = 16

probability that the respondent is female, given that the respondent is concerned about security

                                                                                         = 16/25 = 0.64