Latest TCS Aptitude Question SOLUTION: 4 men throw a die each simultaneously. Find the probability that at least 2 people get the same number.

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(#M40033516) TCS Numerical Ability question Keep an EYE

4 men throw a die each simultaneously. Find the probability that at least 2 people get the same number.

Asked In TCS akshitha (10 years ago)

Unsolved Read Solution (14)

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Read Solution (14) :

priyanka  (10 years ago)

13/18 as 1-(probability of not getting same no.)=1-((6*5*4*3)/(6*6*6*6))

Is this solution Helpfull? Yes (71) | No (12)  

raviteja  (9 years ago)

The first person rolls a die, and gets a number.

The second person has a 5/6 chance of rolling a different number.

The third person has a 4/6 chance of rolling a number different from those two.

The fourth person has a 3/6 chance of rolling a number different from all three.

The odds that no two will roll the same number is 5/6*4/6*3/6 = 5/18 = .2777...

That's the odds that no two will roll the same number, so the odds that two (or more) of them will roll the same number is 1-5/18 = 13/18 = .7222...

Is this solution Helpfull? Yes (65) | No (4)  

Harish  (9 years ago)

1-((6*5*4*3)/6^4)
=1-10/36=13/18

Is this solution Helpfull? Yes (9) | No (1)  

siddu  (8 years ago)

One way to solve it is by considering the opposite - That on throwing the dice 4 times, you never get a pair.

In this case, the probability of what happens on the first throw does not matter. But the probability of getting a different number on the second, third and fourth throw are 5/6, 4/6 and 3/6 respectively.

So on multiplying we get 6/6*5/6*4/6*3/6 = 5/18

On substracting it from 1, we get 1-(5/18) = 13/18

Therefore 13/18 is the correct answer

Is this solution Helpfull? Yes (9) | No (1)  

Arpit Rawat  (10 years ago)

Rakesh pls provide sol. for this

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

NISHANT AGARWAL  (10 years ago)

Probability of atleast two people getting same number is

1/6 * 1/6 = 1/36 (Ans)

Is this solution Helpfull? Yes (5) | No (40)  

swarnalakshmi  (8 years ago)

The possibility of getting any no. is 1.
The probability of getting the same no. again is 1/6.
The probability of getting the same no. 3rd time is 2/6.
similarly, the probability of getting the same no. 4th time is 3/6.
so the ans. is (1*1/6*2/6*3/6)=1/36.

Is this solution Helpfull? Yes (3) | No (6)  

lakshmi mrudula  (8 years ago)

pls...tell the correct answer

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

shireesha  (8 years ago)

Let's first find the probability that all the people get different numbers.

Outcome of each die can be any of the 6 numbers. Therefore,
Total number of outcomes
=
6
4
=64

First die can give any of the 6 numbers
Second die can give any of the remaining 5 numbers
Third die can give any of the remaining 4 numbers
Fourth die can give any of the remaining 3 numbers
Therefore, total favorable outcomes 6×5×4×3

P(all people get different numbers)
=
6
×
5
×
4
×
3
6
4
=
5
18
=6×5×4×364=518

P(at least 2 people get the same number)
=
1
−
5
18
=
13
18
=1−518=1318

Is this solution Helpfull? Yes (1) | No (2)  

SHREYASHREE MUKHOPADHYAY  (7 years ago)

1-((6*5*4*3)/(6^4))

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

mayank  (4 years ago)

By using, 1-(probability of not getting same no. by diiferent people)=1-((6*5*4*3)/(6*6*6*6))
We get the answer as 13/18.
simple...

Is this solution Helpfull? Yes (1) | No   

pranjul chandel  (9 years ago)

Ans is→15180/(6^6)→.325

Is this solution Helpfull? Yes | No (1)  

payal sharma  (8 years ago)

total =6*6*6*probability for none are same=6c1*5c1*4c1
probability atleast 2 are same is 6*6*6-6*5*4=96
ans=96

Is this solution Helpfull? Yes | No (7)  

Deepak  (5 years ago)

Given 4 men throw a die and 2 people get the same number.

1) The first die can give any of the 6 numbers.

2) The Second die can give any of the remaining 5 numbers.

3) The third die can give any of the remaining 4 numbers.

4) The fourth die can give any of the remaining 3 numbers.

So, the total possible outcomes will be = 6 * 5 * 4 * 3.


Probability of all getting different numbers = 6 * 5 * 4 * 3/6^4

                                                                        = 5/18.

The probability of 2 people get the same number = 1 - 5/18

                                                                             = 13/18.

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