Question

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

Answer 1

Answer:

The expected value of winnings is $\dfrac{5}{9}$.

Step-by-step explanation:

There are cards numbered 2 through 10.

the total number of cards 2 through 10 is 9.

$n(S)=9$

The sample spaces for odd cards is,

$2,4,6,8,10$

The total number of the odd card is,

$n(odd)=5$

The sample spaces for even cards is,

$3,5,7,9$

The total number of even card is,

$n(even)=4$

The winning probability is,

$p=\frac{n(odd)}{n(S)}$

Now, substitute the value

$p=\frac{5}{9}$

Hence, the expected value of winning is $\dfrac{5}{9}$.