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

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

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

So, remaining probability would be

Amount paid or value of 4 or less = $165

Amount not paid for other case = $45

So, the expected value would be

Hence, the required expected value is $3.46.

step-by-step explanation:

you can add the two numbers and divide the result by 2. or you can find the gap between the two numbers and add half of this to the smaller number.

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)