Question

If X follows a binomial distribution with parameters n = 10 and p. If 4P(X = 6) = P(X = 4), then p = ______ 

पर्याय

• ${\displaystyle \frac{1}{2}}$

• ${\displaystyle \frac{1}{4}}$

• ${\displaystyle \frac{1}{6}}$

• ${\displaystyle \frac{1}{3}}$

Answer 1

If X follows a binomial distribution with parameters n = 10 and p. If 4P(X = 6) = P(X = 4), then p = ${\displaystyle \underline{\frac{1}{3}}}$.

Explanation:

4P(X = 6) = P(X = 4) 

⇒ ${\displaystyle 4.{}^{10}{\text{C}}_6{\text{P}}^6{\text{q}}^4={}^{10}{\text{C}}_4{\text{P}}^4{\text{q}}^6}$

⇒ 4p² = q²

⇒ 4p² = (1 - p)²

⇒ 3p² + 2p - 1 = 0

⇒ p = ${\displaystyle \frac{1}{3}}$