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

Answer: 0.3439

Step-by-step explanation:

Total number of digits : 10

The number of digits except zero =9

The probability of selecting non-zero number :-

$\dfrac{9}{10}=0.9$

Then, the probability that one such phone number , the last four digits do not include any zero:-

$\text{P(no zero )}=(0.9)^4$

Then , the probability that for one such phone​ number, the last four digits include at least one 0:-

$\text{P(at-least one zero )}=1-(0.9)^4=0.3439$

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