50 red marbles and 50 blue marbles Puzzle
You have two jars, 50 red marbles and 50 blue marbles.
A jar will be picked at random, and then a marble will be picked from the jar. Placing all of the marbles in the jars.
How can you maximize the chances of a red marble being picked?
What are the exact odds of getting a red marble using your scheme?
Seems tricky at first, right ? Given that the number of red and blue marbles are the same, you would tend to think that the odds are 50-50. You would try different combinations, such as 25 of each colored marble in a jar or putting all red marbles in one jar and all the blue in the other. You would still end up with a chance of 50%.
So lets think of a better way to distribute the marbles. What if you put a single red marble in one jar and the rest of the marbles in the other jar? This way, you are guaranteed at least a 50% chance of getting a red marble (since one marble picked at random, doesn’t leave any room for choice). Now that you have 49 red marbles left in the other jar, you have a nearly even chance of picking a red marble (49 out of 99).
So let’s calculate the total probability.
P( red marble ) = P( Jar 1 ) * P( red marble in Jar 1 ) + P( Jar 2 ) * P( red marble in Jar 2 )
P( red marble ) = 0.5 * 1 + 0.5 * 49/99
P( red marble ) = 0.7474
Thus, we end up with ~75% chance of picking a red marble.
Your Answer
More puzzles to try-
100 doors
There are 100 doors, all closed. In a nearby cage are 100 monkeys. The first monkey is let out, and ...Read More »Next Number in the Series Puzzle
Next Number in the Series, 5, 16, 49, 104, ?Read More »Token of love
A thousand coloured folds stretch toward the sky, Atop a tender strand, Rising from the land, ‘Til killed by maiden’s ...Read More »Give the answer of easy aptitude question
Options- (1)16 (2) 9 (3)225 (4)196Read More »Name 3 consecutive days puzzle
Can You Name Three Consecutive Days. Without Using The Words – Monday , Tuesday, Wednesday, Thursday, Friday, Saturday, Or Sunday?Read More »Quarter between the quarters riddle
If you have two quarters on a table touching each other, how can you move one of the quarters without ...Read More »Magic of Maths
Find out a multi-digit number that if multiplied by the number 9 or any of its multiplications products (i.e. 18, ...Read More »Lion and its Tamer
A lion and its tamer are standing inside a cage that measures 1 unit in radius. Both of them can ...Read More »Alternating T-shirt colors
Ten friends walk into a room where each one of them receives a hat. On each hat is written a ...Read More »Unhapppy maths bookk riddle
Why is a math book unhappy?Read More »28 Chickens
There are 30 Cats in a field, and 28 chickens. How many did not ?Read More »What is the smallest possible amount of money ?
A grocer in a small business had managed to put aside (apart from his legitimate profits) little sum in dollar bills, ...Read More »What does the complete addition look like in digits?
In the addition below, all digits have been replaced by letters. Equal letters represent equal digits and different letters represent ...Read More »Find The feeding Time
In a zoo Peter was in charge of feeding all of the animals in the morning. He had a regular schedule ...Read More »Count chocolate and sodas puzzle
A chocolate costs 6 rupees and a soda costs 5 rupees. If you have 32 rupees in total, how many ...Read More »Find the missing Number
Find out the missing number in the picture attached:Read More »What is my aunt’s share?
When my uncle in Madura died recently, he left i will, instructing his executors to divide his estate oi Rs.1,920,000 ...Read More »Compare the 2 images below (composed of 4 half discs). What have they in common?
Sides of Circle
How many sides does a circle have?Read More »Delivery Incentive
John was a very careless driver, so his owner Jacob gave him an offer that he will get an incentive ...Read More »