08. Probability After Sense

09 Probability After Sense V1

In the above scenario, a robot starts out without any information about where it is in a 1D world and has a uniform distribution of location probabilities: [0.2, 0.2, 0.2, 0.2, 0.2]. You can assume this is the initial distribution for the quiz questions below.

If the robot senses that it is in a red square, and its sensor says that there is a 60% chance that this is indeed a red square, what is the combined probability that a robot is sensing red and in a red square?

Another way of asking this is: what is the new probability that the robot is in square x2?
SOLUTION: 0.12

If the robot senses that it has reached a red square, but its sensor says that there is still a 20% chance that this is actually a green square (and the sensor reading is incorrect), what is the combined probability that a robot is sensing red but in a green square?

Another way of asking this is: what is the probability that our robot sense red but is actually in square x1?
SOLUTION: 0.04

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