Complete the two-way frequency table below, which shows the distribution of blood types for students in their first year at a local college.
O A B AB Total
Male (M) 210 174 74 42
Female (F) 315 261 111 63
Total
What is P(F|A), and are the events "the student is female" and "the student has blood type A" independent events?
A: 261/1,250; they are independent because P(F ∩ A) ≠ P(F) ⋅ P(A)
B:87/250; they are dependent because P(F ∩ A) ≠ P(F) ⋅ P(A)
C:3/5; they are independent because P(F ∩ A) = P(F) ⋅ P(A)
D:1/4; they are dependent because P(F ∩ A) = P(F) ⋅ P(A)
+128475 O A B AB Total
Male (M) 210 174 74 42 500
Female (F) 315 261 111 63 750
Total 525 435 185 105 1250
P(F l A ) = 261/435 = 3/5
If independent P(F and A) = P(F) * PA)
P(F and A) = 261 / 1250
P(F) = 750/1250 P(A) = 435/ 1250
So.... P(F) * P( A) = (750/1250) * (435/1250) = 261/1250
So independent
P( F and A) = P(F) * P(A)
So... "C" is correct
