# Choose the Dress

322.6K Views

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?

SherlockHolmes Expert Asked on 15th October 2021 in

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.

Moshe Expert Answered on 21st February 2023.

• ## More puzzles to try-

• ### who answer first riddle

a Judge decided to freed Four criminals without any punishment but after solving a puzzle, as it was a minor ...Read More »
• ### Has two eyes riddle

It is flat as a leaf, round as a ring, Has two eyes, can not see a thing. What is ...Read More »
• ### Coke Riddle

Jacob has 25 dollars, he spends 20 dollars on a Coke. What does he have?Read More »

• ### Chocolates Bricks Riddle

How many steps are required to break an m × n sized bar of chocolate into 1 × 1 pieces? ...Read More »
• ### Word of 3 letters

A word of letters three I know. Add two in this, and fewer there will be. What is it?Read More »
• ### Can you think of what happened inside the interview room?

Rohan was in an interview. The interviewer told his that this was his last question and then he asked him ...Read More »
• ### 2 Cars and bird between them logical math puzzle

There is a circular race-track of diameter 1 km. Two cars A and B are standing on the track diametrically ...Read More »
• ### Making 34 using only 3s

Make 34 using only the number 3. You can also use x, /, + and ().Read More »
• ### Count The Blocks

Can you count the number of blocks in the picture below?Read More »
• ### How many can we place in this manner?

We have a circular dining table made of marble which had come down to us as a family heirloom. We ...Read More »
• ### Promise to president puzzle

Ronald has a rare opportunity to meet the President of the United States. During his visit the president gives him ...Read More »
• ### How the man got busted puzzle

A man can make perfect counterfeit bills. They look exactly like real ones, they’re made of exactly the same materials, ...Read More »
• ### How could i measure 45 minutes ?

I have two rectangular wires. Both of them have property that when i light the fire from one end , ...Read More »
• ### Ship with coins riddle

A pirate ship captures a treasure of 1000 golden coins. The treasure has to be split among the five pirates: ...Read More »
• ### Count the Animals

A cricket has 6 legs, a squirrel has 4 legs and a spider has 8 legs. In a local zoo, ...Read More »
• ### Father & Son riddle

Two fathers and two sons sat down to take tea. They had exactly three cup of tea, each person had ...Read More »
• ### Thin not fat

It can be thin, But not fat; You need it around, it promises not to Crowd you; Some use a ...Read More »
• ### Layers of wall around riddle

A little pool with two layers of wall around it. One white and soft. The other dark and hard. Amidst ...Read More »
• ### Is not a Mermaid riddle

What has beautiful hair, a pretty face, two arms, a fish’s tail, looks like a mermaid, but is not a ...Read More »