From the set x 0 x 1 numbers are selected at random and i

From the set { x | 0 x < 1} numbers are selected at random and independently (and with replacement) and rounded to three decimal places (hence, the three digits are random). What is the probability that 0.345 is obtained

(a) for the first time on selection 1000?

(b) for the third time on selection 3000?

Solution

as the number has to be taken from set { x | 0 x < 1} which inludes number from 0 to 0.999

therefore total numbers will be 1000.

a) 0.345 is the 1 number from the set

probability that selected 1st time = 1/1000 =0.001

b) probability that selected 3 rd time = 2999/3000*2999/3000*1/3000 = 0.0003