Question

If in a binomial distribution \(n=4\), \(P(X=0)=\frac{16}{81}\), then \(P(X=4)\) equals

• A. \(\frac1{16}\)
• B. \(\frac1{81}\)
• C. \(\frac1{27}\)
• D. \(\frac18\)

Hint:

Endpoints in binomial use \(p^n\) and \(q^n\).

Answer 1

The Correct Option is B

Step 1: \[ P(X=0)=q^4=\frac{16}{81}\Rightarrow q=\frac23 \]
Step 2: \[ p=1-q=\frac13 \]
Step 3: \[ P(X=4)=p^4=\frac1{81} \]