You pick a card at random from an ordinary deck of 52 cards. if the card is an ace, you get 9 points; if not, you lose 1 point.



write the equation for the expected value.

e(v) = 452 (a) + b52 (c)

a = b = c =

Step-by-step explanation:

We know that:

In a deck of 52 cards there are 4 aces.

Therefore the probability of obtaining an ace is:

P (x) = 4/52

The probability of not getting an ace is:

P ('x) = 1-4 / 52

P ('x) = 48/52

In this problem the number of aces obtained when extracting cards from the deck is a discrete random variable.

For a discrete random variable V, the expected value is defined as:

Where V is the value that the random variable can take and P (V) is the probability that it takes that value.

We have the following equation for the expected value:

In this problem the variable V can take the value V = 9 if an ace of the deck is obtained, with probability of 4/52, and can take the value V = -1 if an ace of the deck is not obtained, with a probability of 48 / 52

Therefore, expected value for V, the number of points obtained in the game is:

So:

step-by-step explanation:

y = | -2(-2) |     →     y = | 4 |     →     y = 4       ⇒   (-2, 4)

y = | -2(-1) |     →     y = | 2 |     →       y =   2       ⇒   (-1, 2)    

y = | -2(0) |     →     y = | 0 |     →       y = 0         ⇒   (0, 0)

y = | -2(1) |   c →     y = | -2 |     →     y =   2         ⇒   (1, 2)    

y = | -2(2) |     →     y = | - 4 |     →     y =   4         ⇒   (2, 4)  

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4