A box contains 500 red marbles and 600 blue marbles. Marbles will be drawn one a
ID: 3150834 • Letter: A
Question
A box contains 500 red marbles and 600 blue marbles. Marbles will be drawn one at a time from the box. You will win a dollar if more red marbles are drawn than blue marbles. You have the option of drawing either 100 times or 200 times. You also have the option of drawing with replacement or without replacement. Circle one of the choices below. (a) To maximize my chance of winning, I should make 100 draws with replacement. (b) To maximize my chance of winning, I should make 100 draws without replacement. (c) To maximize my chance of winning, I should make 100 draws-but it doesn't matter if I draw with or without replacement. (d) To maximize my chance of winning, I should make 200 draws with replacement. (e) To maximize my chance of winning, I should make 200 draws without replacement. (f) To maximize my chance of winning, I should make 200 draws-but it doesn't matter if I draw with or without replacement. (g) All four methods give me the same chance of winning. (h) I need more information to say which method I should choose.Explanation / Answer
Answer
Here, a Box contains
Red Marbles = 500, Blue Marbles = 600
Total = 500 + 600 = 1100 Marbles
Marbles will draw one at a time. We will win if, red marbles drawn more than blue marbles. We can draw either 100 or 200 times.
Now we will evaluate each option and make conclusion.
Option (a): 100 draws & With Replacement
Probability of getting 51 red out of 100 draws
= (500/1100) * (500/1100) * (500/1100) * …….(51 times)
= (500/1100) ^ (51)
= 3.44 * 10-18
Option (b): 100 draws & Without Replacement
Probability of getting 51 red out of 100 draws
= (500/1100) * (499/1099) * (498/1098) * …….(51 terms)
= 7.96 * 10-19
Option (c):
From option (a) and (b), we can see winning probability with replacement and without replacement is different
Option (d): 200 draws & With Replacement
Probability of getting 101 red out of 200 draws
= (500/1100) * (500/1100) * (500/1100) * …….(101 times)
= (500/1100) ^ (101)
= 2.60 * 10-35
Option (e): 200 draws & Without Replacement
Probability of getting 101 red out of 200 draws
= (500/1100) * (499/1099) * (498/1098) * …….(101 terms)
= 2.29 * 10-38
Option (f):
From option (d) and (e), we can see winning probability with replacement and without replacement is different
Option (g):
From option (a), (b), (d) and (e), we can see winning probability of either 100 or 200 and either with replacement or without replacement is different.
Option (h):
Given data is sufficient to calculate required probability.
So, answer is option (a) To maximize my chance of winning, I should make 100 draws with replacement.
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