wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Write theorem of total probability and prove it.

Open in App
Solution

Theorem of total probability : If A and B two mutually non-exclusive events associated with random experiment then P(A+B)=P(AB)=P(A)+P(B)P(AB)
Proof : Consider the ven diagram in which A and B are two subsets sample spaces shaded portion represents the set AB
Let r,s and t be the number of elementary events in set A,B, and AB and n be the total number of elements of S.
The number of elementary events in the set AB representing the event A and B is equal to =r+st.
P(AB)=r+stn=rn+sntn
=P(A)+P(B)P(AB)
By definition of probability.
665673_628630_ans_9d6e8334bac94c0981273a351b3f0b44.png

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Addition rule
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon