Mathematics for Computer Science
MIT 6.042J/18.062J
Law of Total
Probability
Albert R Meyer,
May 3, 2013
totalprob.1
Law of Total Probability
Law for reasoning
about probability
by cases
Albert R Meyer,
May 3, 2013
totalprob.2
Law of Total Probability

A
B1
B2
Albert R Meyer,
B3
May 3, 2013
totalprob.3
Law of Total Probability
Pr[A] = Pr[B1A] +
Pr[B2A] +
Pr[B3A]
Albert R Meyer,
May 3, 2013
totalprob.4
Law of Total Probability
]
Pr[B
]
Pr[A] =Pr[A|B
Pr[B1A]
+
1
1
Pr[B2A] +
Pr[B3A]
Albert R Meyer,
May 3, 2013
totalprob.5
Law of Total Probability
Pr[A]=Pr[A|B1] Pr[B1]
+ Pr[A|B2] Pr[B2]
+ Pr[A|B3] Pr[B3]
Albert R Meyer,
May 3, 2013
totalprob.6
Law of Total Probability
If  is disjoint union of B0, B1,…
= å Pr[A|Bi] × Pr[B i]
i
Albert R Meyer,
May 3, 2013
totalprob.7