Probability 1

A random-number table consists of a succession of digits each chosen at randomand .
independently from the set {0,1,...,9}
(a)Two successive digits are taken from such a table, find the probability that their .
sum is 9.
Sol.
9=0+9=1+8=…=9+0.
p=10/100=1/10.

(b)Four successive digits are taken from the table. Find the probability thatthe sum of
the first two equals the sum of the third and fourth.
Sol
sum of the first two =0 =>N0=1*1=1
sum of the first two =1 =>N1=2*2=4
…….
sum of the first two =8 =>N8=9*9=81
sum of the first two =9 =>N9=10*10=100
sum of the first two =10 =>N10=9*9=81
........
sum of the first two =19 =>N19=1*1=1
N=1^2+2^2+3^2+…+10^2+9^2+…+1^2
=2*(1^2+2^2+3^2+…+10^2)－10^2
=2*10*(10+1)*(2*10+1)/6－100
=670
p=670/10^4=67/1000

Is repitition allowed?