A satellite system consists of 4 components and the system can function if at
least 2 components are working. If each component independently works with probability
0.8, what is the probability the system will function?
least 2 components are working. If each component independently works with probability
0.8, what is the probability the system will function?
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Use a binomial distribution with n=4 trials and success probability p=0.8:
P(exactly k successes) = (n choose k) p^k (1-p)^(n-k)
= (4 choose k) (0.8)^k (0.2)^(4-k).
P(system works) = P(at least 2 successes)
= P(exactly 2 successes) + P(exactly 3 successes) + P(exactly 4 successes)
= (4 choose 2) (0.8)^2 (0.2)^2 + (4 choose 3) (0.8)^3 (0.2) + (4 choose 4) (0.8)^4
= 6(0.0256) + 4(0.1024) + 0.4096
= 0.1536 + 0.4096 + 0.4096
= 0.9728 .
Lord bless you today!
P(exactly k successes) = (n choose k) p^k (1-p)^(n-k)
= (4 choose k) (0.8)^k (0.2)^(4-k).
P(system works) = P(at least 2 successes)
= P(exactly 2 successes) + P(exactly 3 successes) + P(exactly 4 successes)
= (4 choose 2) (0.8)^2 (0.2)^2 + (4 choose 3) (0.8)^3 (0.2) + (4 choose 4) (0.8)^4
= 6(0.0256) + 4(0.1024) + 0.4096
= 0.1536 + 0.4096 + 0.4096
= 0.9728 .
Lord bless you today!