at least one zero

Question

When four digits (between 0 and 9 inclusive) are randomly selected with replacement for a lottery ticket, at least one of the digits is 0.

 

I need to provide a written description of the complement of the given event, then find the probability of the complement of the given event.

 

The answer in the back of the book is 0.656 and I seriously dont know how they get out.

Answer 1

Four digits (between 0 and 9 inclusive) are randomly selected with replacement for a lottery ticket.

Probability of the event is .

Event is selection of four digits such that at least one digit is zero.

Complement of the event is selection of four digits such that not even one of the digit is zero.

Find the probability of the event that that the digit is not 0.

Probability of the selecting first digit that is not zero is .

Probability of selecting second digit that is not zero (with replacement) is .

Probability of selecting third digit that is not zero (with replacement) is .

Probability of selecting fourth digit that is not zero (with replacement) is .

The four events are independent events then .

Probabilty of selecting four digits such that none of the digit is zero is 0.6561.

Comments

why four times???