Question

If \(X\sim B(10,0.4)\), then the probability that \(X\) takes a value at least 2 is:

• A. \(1-5(0.4)(0.6)^{9}\)
• B. \(1-(0.6)^{9}(4.6)\)
• C. \(1-(0.4)^{10}\)
• D. \(0.66\)

Hint:

Use the complement: P(X >= 2) = 1 - P(X = 0) - P(X = 1).

Answer 1

The Correct Option is B

Step 1: Use the complement
\(P(X\ge 2)=1-P(X=0)-P(X=1)\).

Step 2: Compute the terms
\(P(X=0)=(0.6)^{10}\) and \(P(X=1)=10(0.4)(0.6)^{9}=4(0.6)^{9}\).

Step 3: Combine
\(P(X\ge 2)=1-(0.6)^{9}(0.6+4)\).

Step 4: Simplify
\(=1-(0.6)^{9}(4.6)\).

Final Answer:
The probability is \(1-(0.6)^{9}(4.6)\). \[ \boxed{\text{(B) }1-(0.6)^{9}(4.6)} \]