Answer
(a) $0.215$
(b) $0.9999$
(c) $4$
Work Step by Step
Let $X$ be the random variable of number of calls (out of total of 10 calls) during which the phone lines were occupied. $X$ has the binomial distribution with parameters $n=10, p=0.4$ .
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(a)
$$ \mathbb{P}(X=3) =\left(\begin{array}{c}{10} \\ {3}\end{array}\right) 0.4^{3} 0.6^{7}=[0.215] $$
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(b)
$$\mathbb{P}(X \leq 9) =1-\mathbb{P}(X>9)=1-\mathbb{P}(X=10)=\\ =1-\left(\begin{array}{c}{10} \\ {10}\end{array}\right) 0.4^{10} 0.6^{0}=[0.9999] $$
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(c)
$$\mathbb{E}(X) =n \times p=10 \times 0.4=[{4}] $$
