A bag contains $20$ blue balls and $15$ red balls. In a game, Joe draws $12$ balls one by one, at ra

Question

A bag contains $20$ blue balls and $15$ red balls. In a game, Joe draws $12$ balls one by one, at random and without replacement. The number of blue balls Joe draws from the bag is denoted by $X$. Find $\mathrm{E}\left( X \right)$ and $\mathrm{Var}\left( X \right)$. [4] If $\mathrm{P}\left( X=x \right)$\left( x+a \right)\left( x+b \right)where $a$, $b$, $c$ and $d$ are constants to be determined. Use this inequality to find the number of blue balls that Joe is most likely to draw. [5] Joe plays this game $30$ times. Find the probability that Joe draws at least $10$ blue balls in more than $4$ of his $30$ games. [3]

Accepted Answer

(i) E(X) = 6.86, Var(X) = 1.99; (ii) a=1, b=4, c=20, d=12; mode = 7; (iii) 0.00106

2018 RI CT3 J2 Q13

2018 RI CT3 J2 Q13

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