the host for each party What is the probability of obtaining eight heads in a ro
ID: 3274347 • Letter: T
Question
the host for each party What is the probability of obtaining eight heads in a row when flipping a coin that has a probability of .73 of obtaining a heads on any given flip? Suppose the satellite defense system is established in which eight satellites acting independently have a 0.85 probability of detecting an incoming ballistic missile. a.) What is the probability that at all eight satellites do not detect an incoming ballistic missile? b.) What is the probability that at least one of the eight satellites detects an incoming ballistic c.) Would you feel safe with such a system?Explanation / Answer
4)
Probability of obtaining eight heads in a row = (0.73)^8 = 0.0806
5-a)
Probability that a satellite does not detect an incoming ballistic missile = 1 - 0.85 = 0.15 (let p)
Probability that all eight satellites do not detect an incoming ballistic missile = p^8 = (0.15)^8 = 0.00000026
5-b)
Probability that at least one of the 8 satellites detects an ballistic missile = 1 - (Probability that all eight satellites do not detect an incoming ballistic missile)
Probability that at least one of the 8 satellites detects an ballistic missile = 1 - 0.00000026 = 0.99999974
5-c)
Yes such a system makes feel safe. Because probability of detecting an incoming ballistic missile is almost 1.
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