50 Red Marbles and 50 Blue Marbles | Puzzles for Interview - Interview Preparation PDF Download

Introduction

Imagine you have two boxes, B1 and B2. One box contains 50 red marbles, and the other box contains 50 blue marbles. You need to select one ball randomly from either box and want to maximize the probability of selecting a red ball. Here's how you can do it.

Understanding Probability

Before we dive into the solution, let's understand probability. Probability is the measure of the likelihood of an event occurring. In this case, the event is selecting a red ball from the boxes.

Solution

To maximize the probability of selecting a red ball, we need to reshuffle the marbles in both boxes. Let's calculate the probability of selecting a red ball before and after reshuffling.
Step 1: Before Reshuffling
P(R) = P(B1) * P(B1 | J1) * P(B2) * P(B2 | J2)
Here, P(B1) and P(B2) represent the probability of selecting box B1 and B2, respectively. The probability of selecting each box is 1/2 since we have two boxes of equal size. J1 and J2 represent the total number of balls in B1 and B2, respectively.
If we do not reshuffle any balls, the probability of selecting a red ball would be:
P(R) = ((1 / 2) * 1) * ((1 / 2) * 0) = 0.5

Step 2: After Reshuffling
To maximize the probability of selecting a red ball, we need to decrease the number of red balls in B1 and increase the number of red balls in B2.
Let's take 49 red marbles from B1 and move them to B2. This results in B1 having only 1 red ball and B2 having 49 red balls and 50 blue balls.
Now, the probability of selecting a red ball would be:
P(R) = ((1 / 2) * (1 / 1)) * ((1 / 2) * (49 / 99)) = 0.747474

Conclusion

Thus, by reshuffling the marbles in both boxes, we can increase the probability of selecting a red ball from 0.5 to 0.747474. This simple technique can be used in various scenarios where probability plays a crucial role.