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.