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Given that an opinion poll calls residential telephone numbers at random,

only $20\%$of the calls reach a person.

We watch the random digit dialing machine make $15$calls. $X$is the number that reaches a person

The variable $X$ in this question has a binomial distribution since each subsequent draw is independent of the preceding draw because success is defined as the number reaching a person. The maximum number of calls is set at $15$. The chance of success remains constant at $20\%$. Because the numbers are chosen at random, each draw can be considered independent.

Given that an opinion poll calls residential telephone numbers at random,

only $20\%$of the calls reach a live person. $Y$is the number of calls until the first live person answers

Because there is no set number of components being drawn, the binomial distribution will not be able to produce a good estimate in this case. In anticipation of the first real individual answering, a draw is made.