The following table lists three events obtained from a single run of an electronic…
MATHEMATICS · Multi-part · CBSE · Mathematics · Probability · Probability
Problem
The following table lists three events obtained from a single run of an electronic colour sensor. Each run exactly identifies one dominant colour among Red (R), Green (G) and Blue (B).
Outcome table
Outcome detected : R G B
Assigned probability : 0.40 0.25 0.35
Answer the questions below.
(i) Define the term “exhaustive events” and state the condition their probabilities must satisfy.
(ii) Using the definition in part (i), examine whether the three outcomes listed in the table are exhaustive. Justify your answer with suitable calculation.
(iii) Identify the impossible event and the sure event for this experiment, and write their probabilities.
(iv) If the manufacturer decides to introduce a fourth outcome “No clear dominant colour (N)” that is mutually exclusive with R, G and B, find the probability that must be assigned to N so that the full set of outcomes forms an acceptable probability model.