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Three radar sets, operating independently, are set to detect any aircraft flying through a certain area. Each set has a probability of 0.03 of failing to detect a plane in its area. Consider one of the radar sets. What is the probability that it will correctly detect exactly three aircraft before it fails to detect one, if aircraft arrivals are independent single events occurring at different times?

Sagot :

MrRoyalidn

Answer:

[tex]Probability = 0.00002619[/tex]

Step-by-step explanation:

Given

Let d represents the event that a radar detects an aircraft.

So:

[tex]P(d) = 0.03[/tex]

Required: Determine the probability that a radar detects three before it fails to detect 1.

This event is represented as: d d d d'

And the probability is calculated as thus:

[tex]Probability = P(d) * P(d) * P(d) * P(d')[/tex]

Using complement rule:

[tex]Probability = P(d) * P(d) * P(d) * (1 - P(d))[/tex]

So, we have:

[tex]Probability = 0.03 * 0.03 * 0.03 * (1 - 0.03)[/tex]

[tex]Probability = 0.03 * 0.03 * 0.03 * 0.97[/tex]

[tex]Probability = 0.00002619[/tex]

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