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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)

 Apr 24, 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

 

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 

 

 

cool cool cool

 Apr 24, 2018

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