The table below shows the results of a random sample of patients at a hospital classified by the mutually exclusive categories: gender and blood type.  Blood Type Gender  0 T1 A T2 B T3 AB T4 Total  Female  S1 100 50 25 15   Male  S2 100 25 10 5   Total            a. Complete the table by filling in the correct values in the total column and total row  b. If a person is selected at random from this sample, calculate P(T1|S1) (This means the person has Type O blood given that the person is female) c. If a person is selected at random from this sample, calculate P(S1|T1)  d. If a person is selected at random from this sample, calculate P (T1 and S1) e. Are T1 and S1 independent events?  Use formula to justify answer.

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