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

Probability of the event is .

Find the probability of the complement of the event.

Complement of the event is at least one of the digits is not 0.

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.

Thus, number of motorists did not make an obscene gesture in the previous month is .

50 of the surveyed motorists are randomly selected without replacement.

All the  50 selections are independent and without replacement.

Probability of the first motorist that who did not make an obscene gesture in the previous month is  .

Probability of the second motorist that who did not make an obscene gesture in the previous month is  .

For independent events .

.

For larger values of the population size, sampling formula without replacement is .

Probability of 50 samples without replacement is 0.00486.