contestada

Pooja and Amit are playing a card game with a standard 52 card deck. Pooja will draw a card. If the card she draws is a face card (a jack, queen, or king), she will win $6. If Pooja draws an ace, she will win $4. If any other card is drawn, she will lose $2. The image below shows a standard deck of playing cards.
What is Pooja's expected value of playing this game?

Respuesta :

The probability helps us to know the chances of an event occurring. Pooja's expected value of playing this game is 0.3077.

What is Probability?

The probability helps us to know the chances of an event occurring.

[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

There are 12 face cards, therefore, the probability of the getting a face card can be written as,

[tex]\text{Probability of face card }= \dfrac{12}{52} = 0.2308[/tex]

Also, the winning prize for drawing a face card is $6. Therefore, the expected value will be,

[tex]\text{Expected Value(Face)} = \$6 \times 0.2308= $1.3846[/tex]

There are 4 ace cards, therefore, the probability of the getting an ace card can be written as,

[tex]\text{Probability of ace card }= \dfrac{4}{52} = \dfrac{1}{13} = 0.077[/tex]

Also, the winning prize for drawing an ace card is $4. Therefore, the expected value will be,

[tex]\text{Expected Value(Ace)} = \$4 \times 0.077 = $0.3077[/tex]

There are 36 normal cards, therefore, the probability of the getting a normal card can be written as,

[tex]\text{Probability of normal card }= \dfrac{36}{52} = 0.6923[/tex]

Also, the losing prize for drawing a normal card is -$2. Therefore, the expected value will be,

[tex]\text{Expected Value(Normal)} = (-\$2) \times 0.6923 = -$1.3846[/tex]

Thus, Pooja's expected value of playing this game can be written as,

[tex]\rm Expected\ Value = 1.3846 + 0.3077-1.3846 = 0.3077[/tex]

Hence, Pooja's expected value of playing this game is 0.3077.

Learn more about Probability:

https://brainly.com/question/795909

#SPJ1