Question

If in \(6\) trials, X is a binomial random variable which follows the relation \(9P(x = 4) = P(x = 2)\), then the probability of failure is...

• A. \(0.125\)
• B. \(0.25\)
• C. \(0.375\)
• D. \(0.75\)

Hint:

Write both probabilities with the binomial formula and solve for p/q.

Answer 1

The Correct Option is D

Step 1: Ratio Idea:
Divide $P(X=2)$ by $P(X=4)$: $\dfrac{P(2)}{P(4)}=\dfrac{q^2}{p^2}$ since the binomial coefficients are equal.

Step 2: Use the Condition:
$P(2)=9P(4)$ gives $\dfrac{q^2}{p^2}=9$, so $\dfrac qp=3$.

Step 3: Failure Probability:
$q=\dfrac{3}{3+1}=0.75$. Option (D).

Final Answer:
Option (D). \[ \boxed{\text{(D) } 0.75} \]