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Sagot :
ANSWER
[tex]\text{\$-5}[/tex]EXPLANATION
To find the expected profit, we have to first find the expected payout.
There is a possibility of drawing up to 10 balls, numbered 1 to 10.
There are 5 even balls and 5 odd balls.
We have to find the probabilty of drawing even or odd balls:
=> The probability of drawing an even ball is:
[tex]P(\text{even)}=\frac{5}{10}=\frac{1}{2}[/tex]=> The probability of drawing an odd ball is:
[tex]P(\text{odd)}=\frac{5}{10}=\frac{1}{2}[/tex]The expected payout is the sum of the product of the probability of drawing each ball and the prize of each ball.
That is:
[tex]\begin{gathered} E(X)=\Sigma\mleft\lbrace X\cdot P(X)\mright\rbrace \\ E(X)=(22\cdot\frac{1}{2})+(0\cdot\frac{1}{2}) \\ E(X)=11+0 \\ E(X)=\text{ \$11} \end{gathered}[/tex]The expected profit can be found by subtracting the cost of playing the game from the expected payout:
[tex]\begin{gathered} Exp.Profit=11-16 \\ Exp.Profit=\text{ \$-5} \end{gathered}[/tex]That is the answer.
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