Q3: Two independent satellite-borne sensors are used to determine the extension
ID: 2947042 • Letter: Q
Question
Q3: Two independent satellite-borne sensors are used to determine the extension of inundated areas after a flood. Sensor A has a reliability of 70%, that is, the probability of detecting a pixel (picture element) whose characteristics reflect inundation is 0.7, whereas sensor B has a reliability of 90%. Also, the probability of both sensors detecting a pixel is 0.65. 1. Find the probability that a pixel reflecting inundation is detected, that is, is detected by at least one of the two sensors. Determine the probability that a pixel reflecting flooding is detected by only one sensor. 2.Explanation / Answer
P(A) = 0.7, P(B) = 0.9 and P( A and B) = 0.65
1) First we compute the probabilities here that:
P( A only ) = P(A) - P(A and B) = 0.7 - 0.65 = 0.05
P( B only ) = P(B) - P(A and B) = 0.9 - 0.65 = 0.25
Therefore, using law of addition of probability, we get:
P(A or B) = P(A) + P(B) - P(A and B) = 0.7 + 0.9 - 0.65 = 0.95
Therefore 0.95 is the required probability here.
2) Probability that it is detected by only one sensor (computed in previous part )
= P(A only ) + P(B only ) = 0.05 + 0.25 = 0.3
Therefore 0.3 is the required probability here.
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