1. Understand the binomial distribution:
Given X∼Binomial(n=5,p) and P(X=2)=9P(X=3).
2. Write the binomial probabilities:
P(X=2)=(25)p2(1−p)3=10p2(1−p)3
P(X=3)=(35)p3(1−p)2=10p3(1−p)2
3. Set up the equation:
Given P(X=2)=9P(X=3):
10p2(1−p)3=9⋅10p3(1−p)2
Simplify:
(1−p)=9p⟹1=10p⟹p=101
Correct Answer: (B) 101