Maximize the probability
You have 50 red pen, 50 blue pen, 50 black pen and 3 buckets. One of the buckets is chosen at random and then one pen will be chosen from that bucket at random. How would you maximize the chance of drawing a red pen? What is the probability of doing so?
Give your answer to 3 decimal places.
Assume all 150 pens should be placed in the buckets.
The answer is 0.775.
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1 solution
To maximize 1. You should have to place one red pen into 1st bucket ... By this when we select this bucket P(Red|Bucket1) will be 1 2. one red pen into 2nd Bucket ... By this when we select this bucket P(Red||Bucket2) will be 1 3. Rest all pens should have to place into 3rd bucket ... By this when we select this bucket P(Red|Bucket3) will be 48/148 But P(bucket1)=P(bucket2)=P(bucket3)=1/3 So answer will be P(Bucket1) P(Red|Bucket1) + P(Bucket2) P(Red|Bucket2) + P(Bucket3) P(Red|Bucket3) (1/3) (1) + (1/3) (1) + (1/3) (48/148)