Question

10 balls are marked with digits 0 to 9. If four balls are selected with replacement. What is the probability that none is marked 0?

Answer 1

Let X denote the number of times of getting a ball marked with the digit 0.
P(getting a ball marked with the digit 0) = p = `(1)/(10)`

∴ q = 1 – p = `1 - (1)/(10) = (9)/(10)`

Given, n = 4
∴  X ∼ B`(4, 1/10)` 
The p.m.f. of X is given by

P(X = x) = `""^4"C"_x (1/10)^x (9/10)^(4 - x), x` = 0, 1,...,4
P(none is marked with the digit 0) = P(X = 0)

= `""^4"C"_0 (1/10)^0 (9/10)^4`

= `(9/10)^4`.