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FinnZ [79.3K]
2 years ago
9

Suppose that a satellite defense system is established in which four satellites acting independently each have a 0.9 chance of d

etecting an incoming ballistic missile. a) What is the probability that all 4 satellites will correctly detect the next incoming missile? b) What is the probability that at least one of the four satellites will correctly detect the next incoming missile?
Mathematics
1 answer:
Ne4ueva [31]2 years ago
5 0

Answer: a) 0.6561

b) 0.9999

Step-by-step explanation:

We use Binomial distribution here (Since each satellite is independent of each other.).

In  Binomial distribution :P(x)=^nC_xp^x(1-p)^{n-x}

, where P(X) = probability of getting x successes in n trials.

p= probability of getting success in each trial.

As per given , we have

n= 4

p= 0.9

Let x = Number of  satellites will correctly detect the next incoming missile.

a) The probability that all 4 satellites will correctly detect the next incoming missile:

P(x)=^4C_4(0.9)^4(1-0.9)^{0}

P(x)=(1)(0.9)^4(1)=0.6561

∴the probability that all 4 satellites will correctly detect the next incoming missile=0.6561

b) The probability that at least one of the four satellites will correctly detect the next incoming missile :

P(X\geq1)=1-P(X

∴the probability that at least one of the four satellites will correctly detect the next incoming missile = 0.9999

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