Question

What is the probability of randomly selecting a woman with green eyes and a man with children, P(green-eyed woman and a man with children)?

          WOMEN                      EYE COLOR               CHILDREN

                18                            Brown                                No

                22                            Brown                               Yes

                09                            Blue                                   No

                21                            Blue                                  Yes

                12                            Green                                No

                18                            Green                               Yes

            MEN                            EYE COLOR               CHILDREN

                24                            Brown                                No

                16                            Brown                               Yes

                12                            Blue                                   No

                18                            Blue                                  Yes

                10                            Green                                No

                20                            Green                               Yes

Answer 1

Solution :

We are given the table of women and men and we have to find the probability of randomly selecting a woman with green eyes and a man with children,

Since, green-eyed woman and a man with children are independent, so

P(green-eyed woman and a man with children) = P(green-eyed woman)*P(man with children)

Now,

P(green-eyed woman) = number of green eye woman / total number of woman

                                          = 30/100 = 0.3

and P(man with children) = number of man with children / total number of man

                                         = 54/100 = 0.54

Therefore, P(green-eyed woman and a man with children) = 0.3*0.54 = 0.162

Hence, the probability of randomly selecting a woman with green eyes and a man with children is 0.162