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at a fundraiser, jessie sets up a dice game, ussing 2 normal dice. You pay $.1.50 to play, and get to roll a dice. If you score HIGHER than Jessie's she gives you $2. otherwise you lose. How much profit can she expect to make after playing 40 games

Respuesta :

Answer:

[tex]\$ 26 \frac{2}{3}[/tex]

Step-by-step explanation:

See the attached distribution table:

[tex]P(you\ win)=\frac{5}{12}[/tex]

[tex]P(Jessie\ win)=\frac{7}{12}[/tex]

If you win: Jessie's profit = $1.50 - $2.00

                                         = -$0.50

If Jessie win: Jessie's profit = $1.50

Let's make a probability distribution table of Jessie's profit:

Profit             $-0.50              $1.50

-----------------------------------------------------

P(x)                   [tex]\frac{5}{12}[/tex]                      [tex]\frac{7}{12}[/tex]

[tex]Expectation\ (\mu)=\sum p_ix_i[/tex]

                          [tex]=-0.50\times\frac{5}{12}+1.50\times\frac{7}{12}[/tex]

                          [tex]=\$ \frac{2}{3}[/tex]

[tex]Expectation\ for\ 40\ games=40\times\mu[/tex]

                                           [tex]=40\times\frac{2}{3}[/tex]

                                           [tex]=\$ 26 \frac{2}{3}[/tex]

                                           

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