The following contingency table provides a joint frequency distribution for a ra

Question

The following contingency table provides a joint frequency distribution for a random sample of patients at a hospital classified by blood type and sex. (5 each) 2. Blood Type Total 240 160 400 Sex AB 23 14 37 a. If a patient is selected at random what is the probability that someone has Type 59 71 130 90 60 150 68 15 83 Total A or AB blood and is female? What is the probability that a patient is male if we know they have type B or type AB blood? b. Suppose one of the patients is selected at random. Are the events male and type A blood independent (you must show your work)? c.

Explanation / Answer

a)P(Type A or AB and female) =(90+68)/400=0.395

b) P(male|B or AB blood rgoup) =(14+15)/(37+83)=29/120=0.2417

c)P(male) =160/400=0.40

P(type A) =150/400=0.375

also P(male and type A) =60/400=0.15

cause P(male)*P(type A) =0.40*0.375 =0.15 whcih is equal to P(male and type A)

hence events male and type A are independent.

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