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<p>In a game, $3$ green balls and $7$ yellow balls are placed in a bag. A player draws $4$ balls at random and without replacement. The number of green balls that she draws is denoted by $G$. Find the probability distribution of $G$ and show that $P\left( G\ge 2 \right)=\frac{1}{3}$. Show that $E\left( G \right)=\frac{6}{5}$ and find the variance of $G$.<br></br></p>
<p>Alice scores $5$ points for each green ball that she draws and Bob scores $2$ points for each yellow ball that he draws.<br></br></p>
<p>Alice’s score is denoted by $A$ and Bob’s score is denoted by $B$.<br></br></p>
<p>Without finding the probability distribution of the number of yellow balls, find the expectation and variance of ${A-B}$  if</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Alice and Bob play two separate independent games to decide their scores,</div></li><li><div class="list-item-paragraph">Alice and Bob decide their score in the same game.</div></li></ol>

In a game, $3$ green balls and $7$ yellow balls are placed in a bag. A player draws $4$ balls at random and without replacement. The number of green balls that she draws is denoted by $G$. Find the probability distribution of $G$ and show that $P\left( G\ge 2 \right)=\frac{1}{3}$. Show that $E\left( G \right)=\frac{6}{5}$ and find the variance of $G$.<br></br>

Alice scores $5$ points for each green ball that she draws and Bob scores $2$ points for each yellow ball that he draws.<br></br>

Alice’s score is denoted by $A$ and Bob’s score is denoted by $B$.<br></br>

Without finding the probability distribution of the number of yellow balls, find the expectation and variance of ${A-B}$  if

Constructing and Using Discrete Probability Distributions

Expectation and Variance of Discrete Random Variables

Scaled Random Variables and Sums of Independent Copies

Linear Combinations of Random Variables

Discrete Random Variables (DRV)

<p>In a game, $3$ green balls and $7$ yellow balls are placed in a bag. A player draws $4$ balls at random and without replacement. The number of green balls that she draws is denoted by $G$. Find the probability distribution of $G$ and show that $P\left( G\ge 2 \right)=\frac{1}{3}$. Show that $\mathrm{E}\left( G \right)=\frac{6}{5}$ and find the variance of $G$.</p>
<p>Alice scores $5$ points for each green ball that she draws and Bob scores $2$ points for each yellow ball that he draws.</p>
<p>Alice’s score is denoted by $A$ and Bob’s score is denoted by $B$.</p>
<p>Without finding the probability distribution of the number of yellow balls, find the expectation and variance of $A-B$ if</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Alice and Bob play two separate independent games to decide their scores,</div></li><li><div class="list-item-paragraph">Alice and Bob decide their score in the same game.</div></li></ol>

In a game, $3$ green balls and $7$ yellow balls are placed in a bag. A player draws $4$ balls at random and without replacement. The number of green balls that she draws is denoted by $G$. Find the probability distribution of $G$ and show that $P\left( G\ge 2 \right)=\frac{1}{3}$. Show that $\mathrm{E}\left( G \right)=\frac{6}{5}$ and find the variance of $G$.

Alice scores $5$ points for each green ball that she draws and Bob scores $2$ points for each yellow ball that he draws.

Alice’s score is denoted by $A$ and Bob’s score is denoted by $B$.

Without finding the probability distribution of the number of yellow balls, find the expectation and variance of $A-B$ if

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