Question

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

Answer 1

Answer: 13/18

We will solve this in an easy to understand stepwise manner. Here we go: 

A person will throw a dice, and he will get a number. Now, the probability that the second person will not get the same number is 5/6 (Right? If you don't understand how, ask in the comments). 

Similarly, the probability that the third person will not get the same number is 4/6 and that of the fourth person is 3/6.

Now, what is the probability that all people get different numbers? 

1 × 5/6 × 4/6 × 3/6 = 5/18 


∴ P(at least 2 people get the same number) = 1 - 5/18 = 13/18

Answer 2

Answer:

Probability of 2 people get the same number = $\dfrac{13}{18}$

Step-by-step explanation:

Given :

4 men throw a die each simultaneously.

To Find :

The probability that at least 2 people get the same number.

Solution :

The First Step is :

Find the probability that all the people get different numbers.

So,

First person throws the die and get a number.

As, We know that If one thing/number is taken so, Nobody can again use it.

Now,

Probability  = $\dfrac{5}{6}$

Similary here,

Third person's Probability  =  $\dfrac{4}{6}$

Fourth person's probability  =  $\dfrac{3}{6}$

Remember -

Every People get a different number.

Now,

$\sf \implies P=\dfrac{5}{6}\times\dfrac{4}{6}\times\dfrac{3}{6}=\dfrac{51}{8}$

{ Here All people get different numbers. }

Now,

$\sf \implies P=1-\dfrac{5}{18}\\ \\ \\\sf \implies \dfrac{13}{18}$

{ Here at least 2 people get the same number }

Hence,

Probability of 2 people get the same number = $\dfrac{13}{18}$