Probability
Balls Drawn — Mean of Blue and Yellow
nta_pyq_2024_apr
Grade 12
Question:
Three balls are drawn at random from a bag containing 5 blue and 4 yellow balls. Let the random variables $X$ and $Y$ respectively denote the number of blue and yellow balls. If $\bar{X}$ and $\bar{Y}$ are the means of $X$ and $Y$ respectively, then $7\bar{X}+4\bar{Y}$ is equal to
Step-by-Step Solution
Key Concept: $X+Y=3$ always, so $\bar{X}+\bar{Y}=3$. Mean of hypergeometric: $\bar{X}=\frac{nK}{N}=\frac{3\times5}{9}=5/3$ and $\bar{Y}=\frac{3\times4}{9}=4/3$.
$\bar{X}=5/3$, $\bar{Y}=4/3$. $7\bar{X}+4\bar{Y}=17$.
Correct Answer: 17