Mathematics, 16.02.2021 02:10 kekeke68

The phone lines to an airline reservation system are occupied 61% of the time. Assume that the events that the lines are occupied on successive calls are independent. If 11 calls are placed, what is the probability that the lines are occupied for exactly 5 calls

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Answer from: nosugh

0.1373 = 13.73% probability that the lines are occupied for exactly 5 calls

Step-by-step explanation:

For each call, there are only two possible outcomes. Either the lines are occupied, or they are not. The events that the lines are occupied on successive calls are independent. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

The phone lines to an airline reservation system are occupied 61% of the time.

This means that p = 0.61

If 11 calls are placed, what is the probability that the lines are occupied for exactly 5 calls

This is P(X = 5) when n = 11. So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 5) = C_{11,5}.(0.61)^{5}.(0.39)^{6} = 0.1373$

0.1373 = 13.73% probability that the lines are occupied for exactly 5 calls

Answer from: Quest

you can not drow on this

step-by-step explanation:

Answer from: Quest

a) one student is chosen from classroom a, then a student is chosen from classroom b.

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b. this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes. this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes. this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes. this makes them dependent events.

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