Men with prostate cancer were randomly assigned to undergo surgery (n = 347) or "watchful waiting" (no surgery, n = 348). Over the next several years there were 83 deaths in the first group and 106 deaths in the second group. The results are given in the table.

(a) Let D and A represent died and alive, respectively, and let S and WW represent surgery and watchful waiting. Calculate Pr{D|S} and Pr{D|WW}.
(b) The value of the contingency-table chi-square statistic for these data is χ2s = 3.75. Test for a relationship between the treatment and survival. Use a non directional alternative and let α = 0.05.

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Treatment Surgery WW Total Survival Died 83 106 189 Alive 264 242 506 Total347 348 695