A box contains 10 balls, each marked with one of the digits 0 to 9. If four balls are drawn successively with replacement from the bag, then the probability that none is marked with the digit 0 is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(\left(\displaystyle\frac{9}{10}\right)^4\)
In one draw, 9 of the 10 balls are not marked 0:
\( \displaystyle P(\text{not } 0) = \frac{9}{10} \)
The balls are drawn with replacement, so the four draws are independent and the probabilities multiply:
\( \displaystyle P(\text{none marked } 0) = \left(\frac{9}{10}\right)^4 \)
This is the binomial probability \(P(X = 0)\) with n = 4 and \(p = \frac{1}{10}\).