Question

Subjects for the next presidential election poll are contacted using telephone numbers in which the last four digits are randomly selected (with replacement) find the probability that for one such phone number, the last four digits include at least one 0.

Answer 1

 

Last four digits of the phone numbers are randomly selected (with replacement) for next presidential election
There are 10 numbers (0,1,2,3,0,5,6,7,8,9) for each digit

The probability that a digit other than 0 is selected out  of 10 is,

P(not 0 digit) = 9/10

= 0.9

All the four digits are independent .

So, the probability that all four digits are non-zero is,

P(all four digits are non - zero) = [P(not 0)]^4

=0.9^4

= 0.6561

The probability that at least one of the four digits is,

P(At least one of the four-digit is 0) =1—[P(not zero)]^4

=1-0.6561

=0.3439

approximately 0.344

Therefore, the probability that at least one of the four digits is 0364.