Urn $1$ contains $5$ black balls and $3$ red balls. Urn $2$ contains $4$ black balls and $4$ red bal

Question

Urn $1$ contains $5$ black balls and $3$ red balls. Urn $2$ contains $4$ black balls and $4$ red balls. An experiment is conducted in the following manner: A fair die is tossed. If it shows $1$ or $2$, two balls are drawn from urn $1$ without replacement. Otherwise, one ball is drawn from each urn. Let $X$ be the number of red balls drawn in one experiment. Show that $\mathrm{P}\left( X=0 \right)=\frac{55}{168}$. [1] Find the probability distribution of $X$. Evaluate the expectation and variance of $X$. [6]

Accepted Answer

$E(X) = \frac{5}{6}$, $\text{Var}(X) = \frac{29}{63}$

2005 TJC P2

2005 TJC P2

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