The table below gives the distribution of blood types by sex in a group of 1,200 individuals.
|
Blood Type
|
Male
|
Female
|
Total
|
|
O
|
200
|
416
|
616
|
|
A
|
68
|
284
|
352
|
|
B
|
40
|
144
|
184
|
|
AB
|
12
|
36
|
48
|
|
Total
|
320
|
880
|
1200
|
(Answers for parts a through f can be stated as fractions, such as 35/46, or as decimals rounded to three decimal places)
A person is selected at random from the group.
Showing your work, what the probability is that the person:
(a) is female?
(b) has blood type A?
(c) is a female having blood type A?
(d) is a female or has blood type A?
(e) is female, given that the person's blood type is A?
(f) has blood type A, given that the person is female? Consider the events F = "person is female" and A = "person has blood type A".
(g) Are the events F and A independent? Show work/explain carefully.