Latest ITC Aptitude Question SOLUTION: Q. A father purchases dress for his five daughter. The dresses are of same color but of different size .the dress is kept in dark room. What is the probability that all the three

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Q. A father purchases dress for his five daughter. The dresses are of same color but of different size .the dress is kept in dark room. What is the probability that all the three will not choose their own dress.

Asked In ITC Vignesh (12 years ago)

Unsolved Read Solution (15)

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Read Solution (15) :

tushar ghude  (10 years ago)

correct answer is 1/3 here is most simple way to understand it
how many dresses ? 3 lets say a b c
3 daughters (correct pairs daughter no. 1-a 2-b 3-c)
probability that daughter 1 will choose correct dress (i.e a) is 1/3
probability that daughter 1 will not choose a is 1- 1/3 = 2/3.
remaining dresses 2 out of which only 1 pair is correct (as first daughter picked someone else's dress)
so if either 2 or 3 pick incorrect dress with probability of 1/2 last pair is guaranteed wrong
total probability = 2/3 * 1/2 * 1 = 1/3

Is this solution Helpfull? Yes (83) | No (2)  

sai spandana  (11 years ago)

Total selections=3!=6

Proper Selections: A B C
A C B
C B A
B A C (ie. total 4)

Improper selection: B C A , C A B (ie. total 2)
Probability for improper selection= 2/6 = 1/3
iam sure

Is this solution Helpfull? Yes (77) | No (28)  

$antosh verma  (11 years ago)

ans is 2/3.

as we know (prob)of success+(prob)of fail =1
now according to question ,
probability to choose thier own dress among 3 option will be 1/3 for each daughter.
so, prob of not to choose their own dress according to above formula will be
=>1-1/3
i.e 2/3 ans....

Is this solution Helpfull? Yes (25) | No (50)  

akshat sinha  (8 years ago)

correct answer is 1/3

Method 1)
let 1st girl come and she choose wrong dress so probability of that girl to choose wrong dress out of 3 is =2/3.
now 2nd girl come nd she choose wrong dress so probability of that girl to choose wrong dress out of 2 is 1/2.
now for 3rd girl probability is 1 to choose wrong dress.
so probability tht all the 3 wil not choose der own dress is =2/3*1/2*1=1/3.




method 2)
let A`s dress named A, B dress named B, C`s dress named C.
Then
Total Combinations are 3!=6

A B C
A C B
C B A
B A C
B C A
C A B

Now, We have to find a condition where
A does not choose her dress,
B does not choose her dress and
C does not choose her dress.

In first four condition,
either A or B or C choose either of its right choice
like in ACB, A choose right choice... and so on
but in last two cond.
B C A
C A B
None of them chooses right choice
So fav outcome=2
and total outcome=3!=6
prob-2/6=1/3

Is this solution Helpfull? Yes (16) | No   

palak jain  (11 years ago)

Que: father purchases dress for his three daughters. The dresses are of same colour but of different size .the dress is kept in dark room .What is the probability that all the three will not choose their own dress...

solution: no of ways of choosing dress : 3! = 6
correct way of choosing the dress is only one
so,probability of choosing not the d correct dress = 5/6

Is this solution Helpfull? Yes (14) | No (47)  

Raman  (12 years ago)

Are there five girls or three girls ??

in first line you mentioned five girls.
In qn , you mentioned 'all the three'.

Pls clarify.

Is this solution Helpfull? Yes (13) | No (2)  

deepak srivastava  (11 years ago)

ans is 1-1/3 =2/3
as 1/3 is the probability of occurance of right selection.

Is this solution Helpfull? Yes (10) | No (13)  

Raman  (12 years ago)

In dark, the colour of dress will not matter. As sizes are different , they can easily get own dress as per height.

If the girls are not so smart and they choose dress randomly, then we consider following case.



If there are 3 girls only, then 30% probability that all the three will not choose their own dress...because out of 6 possible arrangements only 2 arrangement are such that all the three will not choose their own dress...

Is this solution Helpfull? Yes (5) | No (13)  

Shanu Dutta  (11 years ago)

ans will be 1/6
for the first girl wrong dresses are 4 out of 5, so probability of choosing the wrong dress is = 2/3
for 2nd = 1/2
for the 3rd = 1/2
so total probability of not choosing own dress is = (2/3)*(1/2)*(1/2)= 1/6

Is this solution Helpfull? Yes (1) | No (5)  

rajesh kumar  (9 years ago)

1st person can choose dress which is correct in 1/3
1st person can choose wrong dress in 1-(1/3) way

2nd person can choose dress which is correct in 1/2
2nd person can choose wrong dress in 1-(1/2) way

that no get correct dress is 2/3*1/3 is 1/3 is answer

Is this solution Helpfull? Yes (1) | No (3)  

munna  (8 years ago)

right ans is 1/5,
1st girl has chances for not choose their own dress =4/5
2nd girl has chances for not choose their own dress =3/4
3rd girl has chances for not choose their own dress =2/3
4th girl has chances for not choose their own dress =1/2
5th girl has chances for not choose their own dress =1
so, probability is =4/5*3/4*2/3*1/2*1= 1/5

Is this solution Helpfull? Yes (1) | No   

Abhishek kumar  (5 years ago)

Let the daughter be A, B, C

let the dresses be 1, 2, 3

1 ⇒

A

A

B

B

C

C

2 ⇒

B

C

A

C

A

B

3 ⇒

C

B

C

A

B

A



Total Cases = 6 Ways

Total Ways by which none gets their own dress = 2

Probability = Successful Outcomes / Total Outcomes = 2 / 6 = 1 / 3

Is this solution Helpfull? Yes (1) | No   

Vignesh  (12 years ago)

Sorry.. its five girls only...

A father purchases dress for his five daughter. The dresses are of same color but of different size .the dress is kept in dark room .What is the probability that all the five will not choose their own dress..

Is this solution Helpfull? Yes | No (10)  

rajesh kumar  (9 years ago)

sory guys a little mistake
1st person can choose dress which is correct in 1/3
1st person can choose wrong dress in 1-(1/3) way

2nd person can choose dress which is correct in 1/2
2nd person can choose wrong dress in 1-(1/2) way

that no get correct dress is 2/3+1/3 is 1/3 is answer

Is this solution Helpfull? Yes | No (3)  

Abhishek Mishra  (8 years ago)

If there are 5 daughters and they pick their dresses simultaneously,
P(picking right dress) bt any daughter =1/5.
for 3 daughters p = 1/5*1/5*1/5.
These three daughters can be choosen from 5 in 5C3 ways
so p = 5c3 *1/125 = 2/25
P9choosing wrong dress) = 1-p(right dress) = 23/25


So pleawswe clarify whether dere are 3 or 5 daughters and if they pick simultaneously or one after other. Because d ans wud change significantly den

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