GATE CS 2017 Set 1 — Question 60
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Engineering Mathematics → Probability & Statistics → Elementary Statistics & Probability
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Question
The probability that a -digit number does NOT contain the digits 0, 5, or 9 is
Correct answer
(C) 0.7^k
Solution
The set of all possible digits is , which has 10 digits.
The digits to be excluded are .
The allowed digits are , which is a set of 7 digits.Assuming each digit position is independent and can be any of the 10 digits with equal probability (ignoring the leading zero constraint for 'number' vs 'string' distinction based on the options provided):The probability of choosing an allowed digit for one position is:For a -digit number, since the choice for each position is independent:
The digits to be excluded are .
The allowed digits are , which is a set of 7 digits.Assuming each digit position is independent and can be any of the 10 digits with equal probability (ignoring the leading zero constraint for 'number' vs 'string' distinction based on the options provided):The probability of choosing an allowed digit for one position is:For a -digit number, since the choice for each position is independent:
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