Question

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 1

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

$\dfrac{12}{52}$

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

So, remaining probability would be

$\dfrac{40}{12}$

Amount paid or value of 4 or less = $165

Amount not paid for other case = $45

So, the expected value would be

$\dfrac{12}{52}\times 165-\dfrac{40}{52}\times 45\\\\=\dfrac{1980}{52}-\dfrac{1800}{52}\\\\=\dfrac{180}{52}\\\\=3.46$

Hence, the required expected value is $3.46.