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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)

hay24  Apr 12, 2018
edited by hay24  Apr 12, 2018
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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

P (F ∩ A ) =  261 / 1250

P(F) * P(A)  =  750/1250 * (435/1250)  = 261 / 1250

So....the events are independent