Help w/ Math question

[kathy2008]

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Question:

A 4-digit number is formed at random from the digit 1,2,3,4 if digits can be repeated in the number, what is the probability that the number is greater than 2500 ?

solve:
the number will be larger than 2,500 if the fist digit is either 3 or 4. Since all digits are selected at random, the probability that a 3 or a 4 is selected for the first digit is 1/2

I am not quite understand the explaination of the book, can anyone help me explain more detail? how can I come up the number 2,500

thanks

 

[dcl222]

so a first digit of a 3 or 4 means 3000+ and 4000+ (you won't have a 2 as a first digit cuz no second number will give you higher than 2500).
so the probability of the first number being a 3 or a 4 will be 1/4 + 1/4 = 2/4 = 1/2
As long as the first number is satisfied, all the other numbers selected at random fits the criteria >2500 so only the 1st number is of importance. I hope that helps

 

[klutzy1987]

1) Well the first number can not be a 1 or a 2 so there are only 2 possibilities for the first number. The other 3 can be any number, so it would be 2*4*4*4=128 Then this is divided by the total possibilities, or 4*4*4*4. So.. 2*4*4*4
4*4*4*4 = the fours all cancel out and the answer would be 2/4 or 1/2