Pulease help A lab has a population of 25 fruit flies of whi

Pulease help!

A lab has a population of 25 fruit flies, of which 5 are black and 20 are grey. A sample of 2 flies is selected. Is the fact that the second selected fly is black independent of the first one being black? Suppose now that there are 10,000 flies in the lab, of which 2,000 are black and 8,000 are grey. A sample of 2 flies is selected. Is the fact that the second selected fly is black independent of the first one being black?

Solution

                       B be the event of drawing black fly in the second draw

                     The total number of flies selected is 25C₂

P(A) =

                                =

                                =

                                =0.2

P(B) =

                          =   

                          =

                         0.16667

                       B be the event of drawing black fly in the second draw

                     The total number of flies selected is 10000C₂

P(A) =

                                =

                                = 0.2

                 P(B) =

                          =   

                          =0.1999

                        

                       B be the event of drawing black fly in the second draw

                     The total number of flies selected is 25C₂

P(A) =

                                =

                                =

                                =0.2

P(B) =

                          =   

                          =

                         0.16667

                       B be the event of drawing black fly in the second draw

                     The total number of flies selected is 10000C₂

P(A) =

                                =

                                = 0.2

                 P(B) =

                          =   

                          =0.1999