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erastovalidia [21]
3 years ago
6

Andy is always looking for ways to make money fast. Lately, he has been trying to make money by gambling. Here is the game he is

considering playing: The game costs $2 to play. He draws a card from a deck. If he gets a number card (2-10), he wins nothing. For any face card ( jack, queen or king), he wins $3. For any ace, he wins $5, and he wins an extra $20 if he draws the ace of clubs.
Create a probability model and find Andy's expected profit per game.
Mathematics
1 answer:
Lorico [155]3 years ago
7 0

Answer:

Option B.

Step-by-step explanation:

Cost of game = $5.00

If they draw a face card, they win $10.00 (i.e. they get their $5.00 back and get an extra $5.00).

Winning amount = $5

Number of face cards = 12

Probability of getting a face card =

If they draw an ace, they win $20.00 (i.e. they get their $5.00 back and get an extra $15.00).

Winning amount = $15

Number of ace = 4

Probability of getting an ace  =

Any other draw they lose their money.

Number of other card (Exclude ace and face cards) = 52-4-12=36

Probability of getting other cards  =

The expected money value playing this game is

E(x) = 5 × P(face cards) + 15 × P(Ace) - 5 × P(Other cards)

The expected money value playing this game is -$1.15

Therefore, the correct option is B.

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<h3>Given:-</h3>

\\ \sf \implies\frac{7 + 3 \sqrt{5} }{3 +  \sqrt{5} }  -  \frac{7  - 3 \sqrt{5} }{3  -   \sqrt{5} }  = a +  \sqrt{5} b \\

<h3>To Find:-</h3>

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<h3>Solution:-</h3>

\\ \sf \implies\frac{7 + 3 \sqrt{5} }{3 +  \sqrt{5} }  -  \frac{7  - 3 \sqrt{5} }{3  -   \sqrt{5} }  = a +  \sqrt{5} b \\

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\\ \sf \implies\frac{( \: 21 - 7 \sqrt{5} \:   +  9    \sqrt{5} - 15) \:  \:  - ( \: 21  + 7 \sqrt{5} \:    -  9    \sqrt{5}  +  15)\: }{(3 +  \sqrt{5})  \:  \:(3 +  \sqrt{5}) }   = a +  \sqrt{5}  \:  b\\

\\ \sf \implies\frac{( \: 6 + 2 \sqrt{5} ) \:  \:  - ( \: 6 - 2 \sqrt{5} )\: }{(3 +  \sqrt{5})  \:  \:(3 +  \sqrt{5}) }   = a +  \sqrt{5}  \:  b\\

\\ \sf \implies\frac{\: 6 + 2 \sqrt{5}  \:  \:  -  \: \: 6 - 2 \sqrt{5} \: }{(3 +  \sqrt{5})  \:  \:(3 +  \sqrt{5}) }   = a +  \sqrt{5}  \:  b\\

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\\ \sf \implies\frac{\: 4 \sqrt{5}  \:  \:   }{ \:  \:  \:  \: 9 - 5 \:  \:  \:   }   = a +  \sqrt{5}  \:  b\\

\\ \sf \implies\frac{\: 4 \sqrt{5}  \:  \:   }{ \:  \:  \:  \: 4 \:  \:  \:   }   = a +  \sqrt{5}  \:  b\\

\\ \sf \implies\frac{\: \cancel{4 } \sqrt{5}  \:  \:   }{ \:  \:  \:  \:  \cancel{4 }\:  \:  \:   }   = a +  \sqrt{5}  \:  b\\

\\ \sf \implies \: \sqrt{5}  = a +  \sqrt{5}  \:  b\\

we can also write it as ;

\\ \sf \implies \: 0 + \sqrt{5}  = a +  \sqrt{5}  \:  b\\

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