If you draw a card with a value of four or less from a standard deck of cards, I will pay you $162. If not, you pay me $45. (Aces are considered the highest card in the deck.) Step 1 of 2 : Find the expected value of the proposition. Round your answer to two decimal places. Losses must be expressed as negative values.

2.77

The expected value is positive, so you expect to gain on average $2.77 per draw.

Explanation:

Define two events

W = winning = getting a card 4 or less

L = losing = getting 5 or higher

P(W) = probability of winning

P(W) = 12/52 since there are 12 cards that are four or less out of 52

P(W) = 3/13 for any suit of 13, there are 3 cards that are four or less

P(L) = 1-P(W)

P(L) = 1-3/13

P(L) = 13/13 - 3/13

P(L) = 10/13

V(W) = net value of winning

V(W) = 162

V(L) = net value of losing

V(L) = -45

E(X) = expected value

E(X) = P(W)*V(W) + P(L)*V(L)

E(X) = (3/13)*162 + (10/13)*(-45)

E(X) = 36/13

E(X) = 2.76923076923077

E(X) = 2.77 rounding to two decimal places (to the nearest cent)

This game is in favor to the player since we got a positive expected value. A fair game would occur if the expected value was 0.

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.