Question

what is the probability of a success for the bolinomial distribution satisfying the following relation 4P(x=4)=P(x=2) and having the parameter n as 6​

Answer 1

Answer:

Step-by-step explanation:

For binomial distribution, P(X=r)=  

n  C  r

​ p  r  (1−p)  n−r  . Here, n =6.

According to question, 4P(X=4)=P(X=2)

⇒4×  6  C  4  p  4  (1−p)  2  =  6  C  2 ​ p  2(1−p)  4 ⇒4×15p  4  (1−p)  2  =15p  2  (1−p)  4 ⇒4p  2  =(1−p)  2  ⇒3p  2  +2p−1=0

⇒3p  

2  +3p−p−1=0⇒3p(p+1)−1(p+1)=0

⇒(p+1)(3p−1)=0

∴ Either p=−1 or p=  3 1

​∵0≤p≤1  

∴p=  3 1

​