you try to guess someones 4 digit atm card number. what is the probability that you will guess it correctly on the first try?

Question

assuming you dont know what it is in advance..

Please explain how you arrived at your answer :)

Answer 1

there are 10 digits: 0,1,2,3,4,5,6,7,8,9

assuming that the digits can be repeated...

for the first choice you pick from 10 digits

for the second choice you pick from 10 digits

for the third choice you pick from 10 digits

for the fourth choice you pick from 10 digits

10*10*10*10=10,000

there are 10,000 4-digit permutations (this means that order is important- 1234 is different from 4321)

the numbers are...

0000

0001

0002

0003

.

.

.

0010

0011

.

.

.

 

0100

0101

0102

.

.

.

9995

9996

9997

9998

9999

there are 10,000 altogether

therefore the probability is 1/10,000