A locker key has 4 digits,3 of which are less than 5 and the other is either 6,7,8 or 9.What is the probability that a random 4 digit number is the key?

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justaguide | College Teacher | (Level 2) Distinguished Educator

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You are only allowed to ask one question at a time. I have changed your question to comply with the same.

The locker key has 4 digits. 3 of the 4 digits are less than 5 and the last digit is either 6, 7, 8 or 9.

The number of combinations we can have with the first 3 digits less than 5 and the last being either of 6, 7, 8 or 9 is 5^3*4 = 500. The digit that is not less than 5 can be either of the four. This makes the total number of combinations 500*4 = 2000.

The number of ways in which a four digit number can be formed is 10^4 as each digit can be either of 0-9.

This makes the probability that any randomly chosen 4 digit number is the locker combination as 2000/10^4 = 2000/10000

The required probability is 0.2