Question

An urn contains 5 blue marbles and 4 red marbles. You draw a certain number of marbles from the urn at random with replacement . . .

(A) You win $243.00 if you draw more blue marbles than red marbles. Assuming that you want to win, which is better: drawing 20 marbles or 200 marbles? Explain your answer briefly.

(B) You win $177.00 if the percentage of red marbles that you draw is less than 42%. Assuming that you want to win, which is better: drawing 10 marbles or 100 marbles? Explain your answer briefly.

Answer 1

In both cases we will be using the concept of the Central limit theorem.

A) Here the percentage of blue marbles is more i.e. 55.56%. Thus according to CLT if we draw more marbles more it will behave like a normal distribution. Thus if we treat success to be picking blue marbles then. Then the probability of selecting more blue marbles than the red marbles will be more as the expected number of selecting blue marbles is more than the red ball. Thus it is better to draw 200 marbles.

B) If we treat success as selecting the red marbles then the expected of re marbles will be 44.44%. thus if we will draw more marbles then greater is the probability to draw number of marbles with a percentage of 44.44% due to CLT. Now we want to draw less than 42% of red marbles. Then it is better to draw 10 marbles because as we will draw 100 marbles the expected number of red marbles will tend to be more than 42 marbles.