The space shuttle flight control system called PASS (Primary Avionics Software Set) uses four independent computers working in parallel. At each critical step, the computers "vote" to determine the appropriate step. The probability that a computer will ask for a roll to the left when a roll to the right is appropriate is 0.003. Let X denote the number of computers that vote for a left roll when a right roll is appropriate. What is the probability mass function of X

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Question:

The space shuttle flight control system called PASS (Primary Avionics Software Set) uses four independent computers working in parallel. At each critical step, the computers "vote" to determine the appropriate step. The probability that a computer will ask for a roll to the left when a roll to the right is appropriate is 0.003. Let X denote the number of computers that vote for a left roll when a right roll is appropriate. What is the probability mass function of X

Answer:[tex]f_X(k)=\binom{4}{k}0.003^k0.997^{4-k}[/tex]Step-by-step explanation:Recall that a probability mass function defined on a discrete random variable X is just a function that gives the probability that the random variable equals a certain value k
[tex]f_X(k)=P(X=k)[/tex]
In this case we have the event “The computer will ask for a roll to the left when a roll to the right is appropriate” with a probability of 0.003.
Then we have 2 possible events, either the computer is right or not.
Since we have 4 computers in parallel, the situation could be modeled with a binomial distribution and the probability mass function
[tex]f_X(k)=\binom{4}{k}0.003^k0.997^{4-k}[/tex]
This gives the probability that k computers are wrong at the same time.

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