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:

if a = 1,   and b = 2, then the answer is 47.99999999. if you round that to the nearest whole number, the answer is 48.

c

step-by-step explanation: