Q66 / 100 · BITSAT 2024 (Memory Based Paper 2) · Mathematics
Given below is the distribution of a random variable $X$
If $\alpha=\mathrm{P}(X \lt 3)$ and $\beta=\mathrm{P}(X\gt2)$, then $\alpha: \beta=$
If $\alpha=\mathrm{P}(X \lt 3)$ and $\beta=\mathrm{P}(X\gt2)$, then $\alpha: \beta=$- A$2: 5$
- B$3: 4$
- C$4: 5$
- Correct answerD$3: 7$
Solution
For a distribution of random variable $x$, $\alpha=P\left(X^6 \lt 3\right)=P\left(X^6=1\right)+P\left(X^6=2\right)$
$\begin{aligned} & =\lambda+2 \lambda=3 \lambda \\ & \text { and } \beta=P\left(X^6 \lt 2\right)=P\left(X^6=3\right)+P\left(X^6=4\right) \\ & =3 \lambda+4 \lambda=3 \lambda \\ & \therefore \quad \alpha: \beta=3: 7\end{aligned}$
Hence, the correct answer is option: 'D'.