Answered

if you draw a card with a value of 4 or less from a standard deck of cards, I will pay you 165$ if not your pay me $45. (Aces are considered the highest card in the deck.)

enter the expected value of the proposition. Round your answer to two decimals

Answer :

Answer: The required expected value is $3.46.

Step-by-step explanation:

Since we have given that

Number of value of 4 or less are

2,3,4

So, there are 12 in numbers.

So, probability would be

[tex]\dfrac{12}{52}[/tex]

Since Aces are considered as the highest card in the deck.

So, remaining probability would be

[tex]\dfrac{40}{12}[/tex]

Amount paid or value of 4 or less = $165

Amount not paid for other case = $45

So, the expected value would be

[tex]\dfrac{12}{52}\times 165-\dfrac{40}{52}\times 45\\\\=\dfrac{1980}{52}-\dfrac{1800}{52}\\\\=\dfrac{180}{52}\\\\=3.46[/tex]

Hence, the required expected value is $3.46.

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