✔ 最佳答案
假設A={兩面都是公的硬幣}, B={兩面都是字的硬幣}
C={公平的硬幣}, D={不公平的硬幣}
Aside:
P(HT)=P(HT|(A & B))*P(A & B)+P(HT|(A & C))*P(A & C)+...
(有AB,AC,AD,BC,BD,CD 6個組合)
P(A & B)=P(A & C)=P(A & D)=P(B & C)=P(B & D)=P(C & D)=2(1/4)(1/3)=1/6
P(HT)=(4/4)*(1/6)+(2/4)*(1/6)+(0.3)*(1/6)+(2/4)*(1/6)+(0.7)*(1/6)+[2(0.3)(0.7)]*(1/6)
=0.57
P(C)=P(C & A)+P(C & B)+P(C & D)
i) 已知擲在地上得出1個H和1個T,
P((A & B)|HT) = P((A & B) & HT)/P(HT)
= P(HT|(A & B))*P(A & B)/P(HT)
=[(4/4)*(1/6)]/0.57
=50/171 (or 0.2923976608)
ii) P(C|HT)=P(C & HT)/P(HT)
=P((C & A) & HT)/P(HT)+P((C & B) & HT)/P(HT)+P((C & D) & HT)/P(HT)
=P(HT|(A & C))*P(A & C)/P(HT)+P(HT|(B & C))*P(B & C)/P(HT)+P(HT|(C & D))*P(C & D)/P(HT)
=[(2/4)*(1/6)]/0.57 + [(2/4)*(1/6)]/0.57 + {[2(0.3)(0.7)]*(1/6)}/0.57
=71/171 (or 0.4152046784)