Question

A bag contains 10 balls each marked with one of the digits 0 to 9. If four balls are drawn successively with replacement from the bag, what is the probability that none is marked with the digit 0 ?

Answer 1

A bag contains 10 balls each marked with one of the digit from 0 to 9. 

Probability that one ball is in marked 0 drawn 

P = 1/10 = 0.1 = 0.1 

Probability that ball is not marked 0 

q = 1 – p 

= 1 – 0.1 = 0.9 

Now 4 balls are drawn successively with replacement. 

∴ Probability that any of them ball is marked 0

= P(X = 0) = 4C₀p⁰q⁴

= (0.9)⁴ = (9/10)⁴