3

Part of 1979 Polish MO Finals

Problems(1)

experiment consists of performing n independent tests

Source: Polish MO Finals 1979 p3

An experiment consists of performing

n

independent tests. The

i

-th test is successful with the probability equal to

p_i

r_k

be the probability that exactly

k

tests succeed. Prove that

\sum_{i=1}^n p_i =\sum_{k=0}^n kr_k.

probabilitycombinatorics