Question

The probability that a k-digit number does NOT contain the digits 0, 5 or 9 is

• A.
  ${0.3}^k$
• B.
  ${0.6}^k$
• C.
  ${0.7}^k$
• D.
  ${0.9}^k$

Answer 1

The correct option is C

${0.7}^k$

Each digit can be filled in 7 ways as 0, 5 and 9 is not allowed.

So each of these places can be filled by 1, 2, 3, 4, 5, 6, 7, 8

So required probability is

${\left(\frac{7}{10}\right)}^{k}or{0.7}^k$