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Assume that each of your calls to a popular radio station
has a probability of 0.02 of connecting, that is, of not obtaining a
busy signal. Assume that your calls are independent.

(a) What is the probability that your first call that connects is
your tenth call?
(b) What is the probability that it requires more than five calls
for you to connect?
(c) What is the mean number of calls needed to connect?

$$P=0.02$$

(a) $$P(x=b)$$

$$P(x=10)=(1-P)^{x-1} P=(1-0.02)^9 \times 0.02=0.0167$$

(b) $$P(x>5)=1-P(x \leq 5)$$

$$x=5,4,3,2,1$$

$$=1-[P(X=1)+P(X=2)+P(X=3)+P(X=4)+P(X=5)]$$

$$=1-\left[0.02+0.98(0.02)+0.98^{2}(0.02)+0.98^{3}(0.02)+0.98^{4}(0.02)\right]=0.904$$

c) $$\mu=\frac{1}{P}=\frac{1}{0.02}=50$$

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