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GATE 2017 EE – Question 5

General Aptitude · Quantitative Aptitude: Probability and Combinatorics · 1 mark · Multiple choice

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

  1. $0.3^k$
  2. $0.6^k$
  3. $0.7^k$
  4. $0.9^k$

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Correct answer: (C) $0.7^k$

Explanation

Each digit must avoid 0, 5 and 9, which leaves 7 of the 10 digits, so each digit has probability 0.7 of being allowed. For $k$ digits the probability is $0.7^k$.