Probability
Probability
nta_abhyas_2025
Grade 12
Question:
NTA Test 16 (Numerical)
If $a_1, a_2, b_1$ and $b_j$ take values in the set $\{1, -1, 0\}$, then the probability that the equation $a_1x + b_1y = 0$ satisfies $\frac{c}{p}$ (p & q are co-prime) then, $q - 2p$ is
Step-by-Step Solution
Key Concept: Calculate cumulative binomial probability by summing individual probabilities for $X = 0, 1, 2$.
Let $X$ be the number of questions a student is unable to solve, with $p = P(\text{unable to answer}) = 1 - \frac{3}{4} = \frac{1}{4}$ and $n = 50$. We need $P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = \binom{50}{0}(\frac{1}{4})^0(\frac{3}{4})^{50} + \binom{50}{1}(\frac{1}{4})^1(\frac{3}{4})^{49} + \binom{50}{2}(\frac{1}{4})^2(\frac{3}{4})^{48} = \frac{16}{4}(\frac{3}{4})^{48}$. Simplifying gives us the answer $40$.
Correct Answer: 40