A card is drawn at random from a deck consisting of cards numbered 2 through 10. A player wins 1 dollar if the number on the card is odd and loses 1 dollar if the number if even. What is the expected value of his winnings

The expected value of winnings is .

Step-by-step explanation:

There are cards numbered 2 through 10.

the total number of cards 2 through 10 is 9.

The sample spaces for odd cards is,

The total number of the odd card is,

The sample spaces for even cards is,

The total number of even card is,

The winning probability is,

Now, substitute the value

Hence, the expected value of winning is .