Boduszewox6

2021-11-18

A radar center consists of two units operating independently. The probability that one of the units detects an incoming missile is 0.99, and the probability that the other unit detects it is 0.95. What is the probability that
(i) both units will detect?
(ii) at least one will detect?
(iii) neither will detect?

Dona Hall

Given data,
The probability that one of the units detects an incoming missile is 0.99.
The probability the other unit detects an incoming missile is 0.95.
Step 1
Here,
The probability that one of the units detects an incoming missile is,
$P\left(first\right)=0.99$
The probability the other unit detects an incoming missile is,
$P\left(second\right)=0.95$
a)The probability that both units will detect are,
$P\left(both\right)=P\left(first\right)×P\left(second\right)$
$=0.99×0.95$
$=0.9405$
Hence, the required probability is 0.9405.
Step 2
b)The probability that at lest one will detect units will detect are,
$P\left(\text{at least 1}\right)=P\left(first\right)+P\left(second\right)-P\left(both\right)$
$=0.99+0.95-0.9405$
$=0.9995$
Hence, the required probability is 0.9995.
c)The probability that neither units will detect the missile,
$P\left(none\right)=1-P\left(both\right)$
$=1-0.9405$
$=0.0595$
Hence, the required probability is 0.0595.

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