Hi I am stuck on this probability question and don't know what to do. Q. A survey is carried out on a computer network. The probability that a log on to the network is successful is 0.92. Find the probability that exactly five out of nine users that attempt to log on will do so successfully.

Gavyn Whitehead 2022-09-12 Answered
Hi I am stuck on this probability question and don't know what to do.
Q. A survey is carried out on a computer network. The probability that a log on to the network is successful is 0.92. Find the probability that exactly five out of nine users that attempt to log on will do so successfully.
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Answers (1)

Savanah Morton
Answered 2022-09-13 Author has 15 answers
The probability of an event A happening excactly k times using the Fundamental Principle of Multiplication in couting is:
P = P ( A ) k
But this event happens out of n tries, so we must also add the probability of not getting the event which is :1−P(A), and the latter happens n−k times and using the same principle we get:
P = ( 1 P ( A ) ) ( n k )
Now to get the total probability we apply the same principle for the two to get:
p = ( 1 P ( A ) ) ( n k ) P ( A ) k
But this can happen in different arrangement or in a different order and so we must include them too, all we have to do now is multiply our probability by the number of times it can occur, which is:
n = n ! k ! ( n k ) !
We finally get:
P = n ! k ! ( n k ) ! ( 1 P ( A ) ) ( n k ) P ( A ) k
Can you apply the same technique for this problem?

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