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Setler79 [48]
3 years ago
6

A person creates a game in which a person pays $5.00 to play. Then, they draw a single card from a standard shuffled deck of car

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

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

With any other draw they lose their money.

What is the expected money value playing this game?


-$5.00

-$1.15

$1.31

$0.38

Mathematics
2 answers:
bekas [8.4K]3 years ago
4 0

Answer:

-$1.15

Step-by-step explanation:

probability to draw a face card: 12/52

probability to draw an ace: 4/52

probability to lose: (52 - 16)/52 = 36/52

The expected money value is the sum of all possible outcomes, each multiplied by the probability of its occurrence.

$5.00*12/52 + $15.00*4/52 - $5*36/52 = -$1.15

valkas [14]3 years ago
3 0

Answer:

Step-by-step explanation:

The expected value is the probability of an event multiplied by the number of times the event happens. And if there is more than 1 event, the expected value is the sum of those.

There are 52 cards in a deck.

There are 12 face cards in a deck. (gain 10)

There are 4 ace in a deck. (gain 20)

Any other card is 36 of them. (lose 5)

The probability of face card is 12/52

The probability of ace is 4/52

The probability of any other card is 36/52

Thus the expected values is:

(12/52)(10) + (4/52)(20) + (36/52)(-5) = $0.38

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Given:

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Using properties of exponents, we get

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On comparing both sides, we get

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substitution and elimination means that you need to use one equation and substitute it in place of some variable in the other equation.

Consider the above two equations.

Take equation 1, which is 4x-2y=22 => x=(22+2y)/4

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