Latest TCS Aptitude Question SOLUTION: Four people each roll a die once. Find the probability that at least two people will roll the same number?

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Four people each roll a die once. Find the probability that at least two people will roll the same number?

Asked In TCS Koyel K (9 years ago)

Solved rahul gera Read Solution (5)

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rahul gera  (9 years ago) Best Solution

atleast 2 means
1-p(no one has same number)
p(no person has same number)=6*5*4*3/6^4=10/36
reqd probability=1-10/36
=26/36=13/18

Is this solution Helpfull? Yes (23) | No (6)  

Monster  (9 years ago)

For at least 2 there will be 3 cases
case 1 : 2 people having same number on dice 1/6*1/6*5/6*5/6,
as these 4 can be arranged in 4P2 ways net probability is 150/6^4
case 2 : 3 people having same number on dice, we get 20/6^4
case 3 : 4 people having same number , 1/6^4
hence ans is 171/6^4 or (4P2+4P3+4P4)/6^4

Is this solution Helpfull? Yes (4) | No (6)  

raviteja  (9 years ago)

4c2+4c3+4c4/6^4

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Azizul Rehman  (9 years ago)

Two are same: 4c2
Three are same: 4c3
all Four are same: 4c4
Total chances: 6^4
so;
4c2+4c3+4c4/6^4

Is this solution Helpfull? Yes (3) | No (7)  

himanshi  (9 years ago)

total ways-no of ways when all nos are different=no of ways when atleast two people have same no
so this will be=
6c1*6c1*6c1*6c1 - 6c1*5c1*4c1*3c1
probability= this expression divided by total ways
ans= 6c1*6c1*6c1*6c1 - 6c1*5c1*4c1*3c1 / 6c1*6c1*6c1*6c1 = 13/18

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