Question

Let \(X\sim B(n,p)\). If \(E(X) = 2\) and \(\text{Var}(X) = 1\), then the probability of getting at most one success is .....

• A. \(0.0625\)
• B. \(0.2500\)
• C. \(0.3125\)
• D. \(0.6875\)

Hint:

Use $np=2$ and $npq=1$ to find $n$ and $p$.

Answer 1

The Correct Option is C

Step 1: List the cases
$P(X=0)=\frac1{16}=0.0625$ and $P(X=1)=\frac4{16}=0.25$. Sum $=0.3125$. Option (C).

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