Question

There are 100 cards in a hat, numbered 1 to 100. The game is to draw one card out of number you draw is odd, you win $19. If the number you draw is even, you win nothing. If you play the game, what is the expected payoff?

Answer 1

As the total odd numbers from 1 to 100 is 50 and the total even number is 50. The probability of get an odd number and the probability of get an even number is the same:

`\begin{gathered} P(\text{odd)}=(50)/(100)=(1)/(2)=0.5 \\ \\ P(\text{even)}=(50)/(100)=(1)/(2)=0.5 \end{gathered}`

Then, the expected is a probability of 50% $19 and a probability of 50% $0