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# The phone lines to an airline reservation system are occupied 40% of the time. Assume that the events that the lines are occupied on success

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The phone lines to an airline reservation system are occupied 40% of the time. Assume that the events that the lines are occupied on successive calls are independent. Assume that 10 calls are placed to the airline.

a.  What is the probability that for exactly three calls the lines are occupied?

b. What is the probability that for at least one call the lines are not occupied?

yuhki  Nov 21, 2014
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The phone lines to an airline reservation system are occupied 40% of the time. Assume that the events that the lines are occupied on successive calls are independent. Assume that 10 calls are placed to the airline.

a.  What is the probability that for exactly three calls the lines are occupied?

10C3* 0.4^3*0.6^7

$${\left({\frac{{\mathtt{10}}{!}}{{\mathtt{3}}{!}{\mathtt{\,\times\,}}({\mathtt{10}}{\mathtt{\,-\,}}{\mathtt{3}}){!}}}\right)}{\mathtt{\,\times\,}}{{\mathtt{0.4}}}^{{\mathtt{3}}}{\mathtt{\,\times\,}}{{\mathtt{0.6}}}^{{\mathtt{7}}} = {\mathtt{0.214\: \!990\: \!848}}$$

b. What is the probability that for at least one call the lines are not occupied?

1-P(all are cccupied)=$${\mathtt{1}}{\mathtt{\,-\,}}{{\mathtt{0.4}}}^{{\mathtt{10}}} = {\mathtt{0.999\: \!895\: \!142\: \!4}}$$

Melody  Nov 22, 2014