Question

PLEASE HELP ME FIX THIS TABLE AND ANSWER THE QUESTION

Answer 1

Explanation

In this problem, the random variable is X, the amount of winnings.

From the statement, we know that:

• the theatre group sells 100 tickets for $5 each,

,

• you purchase 4 tickets,

,

• the prize worth is $150.

Part (d)

• The net amount of profit is X (profit) = -5 * $4 + $150 = -$20 + $150 = $130.

,

• The net amount of losing is X (loss) = -5 * $4 = -$20.

,

• The probability of profit is:

$P(profit)=\text{ }\frac{\#\text{ of tickets bought}}{#\text{ of tickets }}=\frac{4}{100}=0.04.$

• The probability of losing is:

$P\left(loss\right)=1-P\left(profit\right)=1-0.04=0.96.$

• The mean value of profit is:

$x(profit)\times P(x=profit)=\text{ \ 130}\times0.04=\text{ \ 5.2.}$

The mean value of the loss is:

$x(loss)\times P(x=loss)=\text{ -\ 20}\times0.96=-\text{ \ 19.2.}$

Using these data, we complete the table:

Part (e)

If this event is repeated often and you repeat the strategy, the expected average winnings per raffle will be:

$\text{ Average = }x(profit)\times P(x=profit)+x(loss)\times P(x=loss)=\text{ 5.2 + \lparen-19.2\rparen = -14.}$Answer

Part (d)

Part (e):

-14