BISC 202 Lecture Notes - Lecture 6: Mutual Exclusivity, Genetic Counseling, Product Rule

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Calculating probabilities (for pedigrees and other genetic predictions: produ(cid:272)t rule (cid:894)multipl(cid:455) and(cid:895) (cid:862)pro(cid:271)a(cid:271)ilit(cid:455) of i(cid:374)depe(cid:374)de(cid:374)t e(cid:448)e(cid:374)ts o(cid:272)(cid:272)urri(cid:374)g together is the produ(cid:272)t of the pro(cid:271)a(cid:271)ilities of the i(cid:374)di(cid:448)idual e(cid:448)e(cid:374)ts(cid:863) Pro(cid:271)a(cid:271)ilit(cid:455) of o(cid:374)e e(cid:448)e(cid:374)t and a second event both occurring together. (cid:862)pro(cid:271)a(cid:271)ilit(cid:455) of either of t(cid:449)o mutually exclusive events occurring is the sum of their individual pro(cid:271)a(cid:271)ilities(cid:863) Pro(cid:271)a(cid:271)ilit(cid:455) of o(cid:374)e or the other e(cid:448)e(cid:374)t o(cid:272)(cid:272)urri(cid:374)g: cha(cid:374)(cid:272)e of (cid:1008) or (cid:1009) o(cid:374) o(cid:374)e die is (cid:1005)/(cid:1010) + (cid:1005)/(cid:1010) = (cid:1006)/(cid:1010) Sum versus product rules: produ(cid:272)t rule fo(cid:272)uses o(cid:374) out(cid:272)o(cid:373)es a a(cid:374)d b, u(cid:373) rule fo(cid:272)uses o(cid:374) out(cid:272)o(cid:373)es a or b. Pro(cid:271)a(cid:271)ilit(cid:455) of rolli(cid:374)g either t(cid:449)o (cid:1008)s or t(cid:449)o (cid:1009)s. We k(cid:374)o(cid:449) (cid:272)ha(cid:374)(cid:272)e of t(cid:449)o (cid:1008)s is (cid:1005)/(cid:1007)(cid:1010) Cha(cid:374)(cid:272)e of t(cid:449)o (cid:1009)s is the sa(cid:373)e (cid:1005)/(cid:1007)(cid:1010) Cha(cid:374)(cid:272)e of t(cid:449)o (cid:1008)s or t(cid:449)o (cid:1009)s is (cid:1005)/(cid:1007)(cid:1010) + (cid:1005)/(cid:1007)(cid:1010) = (cid:1005)/18. Note: for the latter e(cid:454)a(cid:373)ple (cid:894)su(cid:373) rule(cid:895) the e(cid:448)e(cid:374)ts are (cid:862)(cid:373)utuall(cid:455) e(cid:454)(cid:272)lusi(cid:448)e(cid:863) i. e. if o(cid:374)e event occurs, the other cannot occur.

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