JEE Main 2022 · 30 June · morning · Single correct · +4 / −1
If a random variable X follows the Binomial distribution B(5, p) such that P(X = 0) = P(X = 1), then P(X = 2)/P(X = 3) is equal to :
- (a) 1
- (b) 10
- (c) 25
- (d) 5
Answer and solution
Answer (d) 5
Solution
Maths sir · 3 steps
Use the given equality to get q/p first; then the ratio collapses, because C(5, 2)=C(5, 3).
- Use the condition. With q = 1 - p, P(X=0) = q⁵ and P(X=1) = C(5, 1)pq⁴ = 5pq⁴. Setting them equal and cancelling q⁴ gives q = 5p.
- Find p. Since p + q = 1, p + 5p = 1, so p = 1/6 and q = 5/6.
P(X=2)/P(X=3) = C(5, 2)p²q³/C(5, 3)p³q² = 10/10·q/p = q/p
- So. The ratio is q/p = (5/6)/(1/6) = 5, which is option (d).
The idea to keep. For a binomial, a ratio of neighbouring probabilities is C(n, r)/C(n, r+1)·q/p. Find q/p from the given condition and you rarely need p itself.
Answer from the NTA final answer key. Solution by PrepWiser.