Question

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

Answer 1

Answer: 0.3439

Step-by-step explanation:

Given :The last four digits for telephone numbers are randomly selected​ (with replacement).

Here , each position can be occupied with any of the digit independently .

Total digits = 10

Total digits other than 0 = 9

For each digits , the probability that it is not 0 = $\dfrac{9}{10}=0.9$

If we select 4 digits , The probability of getting no 0 =$(0.9)^4 =0.6561$

(By multiplication rule of independent events)

Now , the probability that for one such phone​ number, the last four digits include at least one 0. = 1- P(none of them is 0)

=1- 0.6561=0.3439

Hence, the probability that for one such phone​ number, the last four digits include at least one 0. is 0.3439 .