headhoncho
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(A|M), and are the events "the student is male" and "the student has blood type A" independent events?
A)start fraction 2 over 5 end fraction; they are independent because P(A ∩ M) ≠ P(M) ⋅ P(A)
B)start fraction 87 over 625 end fraction; they are dependent because P(A ∩ M) ≠ P(M) ⋅ P(A)
C)start fraction 87 over 250 end fraction; they are independent because P(A ∩ M) = P(M) ⋅ P(A)
D)start fraction 1 over 4 end fraction; they are dependent because P(A ∩ M) = P(M) ⋅ P(A)
+128407 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 (A / M) = "probability that the student has blood type A given a male" = 174 / 500 = 87 / 250
P(A ∩ M) = P(A) * P(M) =
174/1250 = (435/1250) * ( 500/ 1250 )
87/625 = 87/625
"C" must be correct.......
