Question

A pair of dice is thrown 4 times. If getting a doublet is considered a success. find the probability of two successes​

Answer 1

Answer:

Step-by-step explanation:

The experiment is to toss a pair of dice (n=4) times. Getting a doublet is considered a success. It is a case of Bernoulli trials.

When a pair of dice is thrown once, the number of possible outcomes = 6×6=36.

The number of possible doublets in this case is :

{(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)}

P(getting a doublet on a roll of two dice) = p=  

36

6

​  

=  

6

1

​  

 

P(not getting a doublet ) = q=1−p=  

6

5

​  

 

X is a binomial distribution.

Here, n=4,p=  

6

1

​  

,q=  

6

5

​  

 

Since X has a binomial distribution, the probability of x successes in n-Bernoulli trials,

P(X=x)=n  

C

​  

 

x

​  

.p  

x

.q  

n−x

 

P(X=2)=4  

C

​  

 

2

​  

 

times(  

6

1

​  

)  

2

×(  

6

5

​  

)  

2

 

=6×  

36

1

​  

×  

36

25

​  

=  

216

25

​