Choose the Dress
A mother bought three dress for her triplets daughters(one for each) and put the dresses in the dark. One by one the girls come and pick a dress.
What is the probability that no girl will choose her own dress?
Let’s assume that the three dresses are indistinguishable and that each girl picks a dress at random. There are 3! = 6 ways that the girls can pick the dresses, since each girl can pick from any of the three dresses, and there are 3 ways to assign the first girl’s choice, 2 ways to assign the second girl’s choice (since one dress is already chosen), and 1 way to assign the third girl’s choice (since two dresses are already chosen).
Out of these 6 possible ways, we need to count the number of ways that no girl picks her own dress. We can use the principle of inclusion-exclusion to do this.
Let A, B, and C denote the events that the first, second, and third girl, respectively, picks her own dress. Then, we want to calculate the probability of the event not(A or B or C), which is the complement of the event A or B or C. By the principle of inclusion-exclusion, we have:
P(not(A or B or C)) = 1 – P(A or B or C) = 1 – (P(A) + P(B) + P(C) – P(A and B) – P(A and C) – P(B and C) + P(A and B and C))
Since each girl picks a dress at random, we have:
P(A) = 1/3 P(B) = 1/2 (since one dress is already chosen, the second girl has only 2 choices) P(C) = 1 (since there is only one dress left for the third girl)
Also, we have:
P(A and B) = 1/3 * 1/2 = 1/6 P(A and C) = 1/3 * 1/1 = 1/3 P(B and C) = 1/2 * 1/1 = 1/2
Finally, we have:
P(A and B and C) = 1/3 * 1/2 * 1/1 = 1/6
Substituting these values into the formula above, we get:
P(not(A or B or C)) = 1 – (1/3 + 1/2 + 1 – 1/6 – 1/3 – 1/2 + 1/6) = 1/3
Therefore, the probability that no girl will choose her own dress is 1/3.
Your Answer
More puzzles to try-
It is confusing
It could be confusing. It could be frustrating. It could be good. It could be funny. What is it ?Read More »Where is Thomas going wrong?
Thomas has missed an excessive number of days of school, so he must meet with Principal Davis. Mr. Davis asks ...Read More »Who will get the banana first
A monkey, a squirrel, and a bird are racing to the top of a coconut tree. Who will get the ...Read More »Fox, Chicken and corn river crossing popular puzzle
A man lives in a small house with a farm as his back garden and has a river beside his ...Read More »The Gravity on Mars
Two Martians and two Earthlings traveling together came to a canal. As a result of the gravity on Mars, the ...Read More »Dry while in the Ocean
It can be half without getting thinner. It can shine with no fire. It can be hidden but never taken. ...Read More »Where is the missing amount??
Two women were selling marbles in the market place —one at three for a paise and other at two for ...Read More »Can you identify the color of the servant who is speaking the truth?
The king of Octopuses has servants who have six, seven or eight legs. The distinguishing characteristics of the servants is ...Read More »Age of ship and boiler
New Zealand to Tahiti. I was curious to look around the ship one day and in the boiler room I ...Read More »Sherlock shoots the pilot riddle
Detective Sherlock entered a restaurant, he heard a voice coming from the kitchen of the restaurant “No Andrew, Don’t shoot“. ...Read More »Rain Drop Measuring
A rain drop fell from one leaf to another leaf and lost 1/4th of its volume. It then fell to ...Read More »Make the Vegetable Riddle
The following four words might seem abrupt to you. But you can make them meaningful by just adding vowels. RDSH ...Read More »Two backbones
Only two backbones and a thousand ribs. What is this?Read More »Four-Word Form Energy
I am a five-letter word and people eat me. If you remove the first letter I become an energy form. ...Read More »Bus interesting puzzle
You are driving a bus. Six people get on, two people get off, then ten people get on and five ...Read More »Seven-League Boots
Meanwhile, back at the castle, the ogre found that the boots he had picked at random from his dark storeroom ...Read More »Missing Letters
Find the missing letters which complete the group. B, C, D, E, ?, P, T, ?Read More »Always up never down
It goes up and never comes down no matter how hard you wish. As it get higher, more wrinkles crawl ...Read More »What is the shortest possible time to fry 3 steaks?
It takes 10 minutes to fry one steak – 5 minutes from each side. Two steaks can fit on a ...Read More »Helper all the time
You use it everyday but let it rest at night. It has an identical twin beside it all the time. ...Read More »