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Home » Assume that on an average one telephone number out of 15, called between 3 p.m. on weekdays, will be busy. What is the probability that if six randomly selected telephone numbers are called, at least 3 of them will be busy?
Assume that on an average one telephone number out of 15, called between 3 p.m. on weekdays, will be busy. What is the probability that if six randomly selected telephone numbers are called, at least 3 of them will be busy?
Binomial Distribution | CBSE | Class 12 | Exercise 32A | Maths | RS Aggarwal
Assume that on an average one telephone number out of 15, called between 3 p.m. on weekdays, will be busy. What is the probability that if six randomly selected telephone numbers are called, at least 3 of them will be busy?

The probability that the called number is busy is \frac{1}{15}
Using Bernoulli’s Trial we have,
\begin{array}{l} P(\text { Success }=x)={ }^{n} C_{x} \cdot p^{x} \cdot q^{(n-x)} \\ x=0,1,2, \ldots \ldots . . . \text { and } q=(1-p), n=6 \end{array}
The probability that at least three of them will be busy is:-
\begin{array}{l} P(0)+P(1)+P(2)+P(3) \\ \Rightarrow{ }^{6} C_{0}\left(\frac{1}{15}\right)^{0}\left(\frac{14}{15}\right)^{6}+{ }^{6} C_{1}\left(\frac{1}{15}\right)^{1}\left(\frac{14}{15}\right)^{5}+{ }^{6} C_{2}\left(\frac{1}{15}\right)^{2}\left(\frac{14}{15}\right)^{4}+{ }^{6} C_{3}\left(\frac{1}{15}\right)^{3}\left(\frac{14}{15}\right)^{3} \\ \Rightarrow 1-\left(\frac{14}{15}\right)^{4} \cdot\left(\frac{59}{45}\right) \end{array}

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