By signing in you confirm you are 18 or older, or have your parent’s or guardian’s consent.

NDA 2 2025 Maths, question 116

Topic: Probability

Q116

Let XX be a random variable following binomial distribution with parameters n=5n=5 and p=kp=k. Further, P(X=1)=0.4096P(X=1)=0.4096 and P(X=2)=0.2048P(X=2)=0.2048. What is the value of kk?

  1. (a) 0.20.2Correct answer
  2. (b) 0.250.25
  3. (c) 0.30.3
  4. (d) 0.350.35

Solution.

Answer: (a) 0.20.2

  1. For a binomial variable, P(X=2)/P(X=1)=[C(5,2)/C(5,1)]k/(1−k)=2k/(1−k).
  2. The supplied ratio is 1/2, giving 4k=1−k and k=0.2.
  3. Check: 5(0.2)(0.8)⁴=0.4096 and 10(0.2)²(0.8)³=0.2048.