Binomial probability on ports. 10 ports. P1,P2,P3...P10 are connected to a computing device which polls them in order to check which is ready. 3 ports out of 10 are ready when we start the cycle. What is the probability that P1,P2 is not ready, and P3 is ready?

Natalya Mayer

Natalya Mayer

Answered question

2022-09-08

Binomial probability on ports
10 ports. P1,P2,P3...P10 are connected to a computing device which polls them in order to check which is ready. 3 ports out of 10 are ready when we start the cycle. What is the probability that P1,P2 is not ready, and P3 is ready?

Answer & Explanation

Waylon Jenkins

Waylon Jenkins

Beginner2022-09-09Added 17 answers

Step 1
We will assume that all combinations of three ports are equally likely to be the ones that are ready. The probability that Port 1 is not ready is 7 10 .
Step 2
Given that Port 1 is not ready, the probability that Port 2 is not ready is 6 9 , Given that 1 and 2 are not ready, the probability Port 3 is ready is 3 8 . Multiply.
Liam Keller

Liam Keller

Beginner2022-09-10Added 4 answers

Step 1
In any case, you should ask yourself, out of all combinations of 3 ones and 7 zeros, how many start with 001. And since the remaining 7 digits consist of 2 ones and 5 zeros, the number of permutations that start with 001 is ( 7 2 ) .
Step 2
Bottom line:
( 7 2 ) = 7 ! 2 ! 5 ! = 21
( 10 3 ) = 10 ! 3 ! 7 ! = 120
So the overall probability is 21 120 = 0.175

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