Answer to Question #304832 in Statistics and Probability for Mathic7284

Question

Daniel went to the perya and played a game. The rule says that the outcome of the game is a random variable 

from 1 to 14 and that if the outcome is even, he wins ₱50. If the outcome is odd, he wins nothing. Assuming that 

playing is for free, what is Daniel’s expected gain, if there is any?

Answer 1

There are 7 odd numbers and 7 even numbers

$$P(X=odd)=\dfrac{7}{14}=\dfrac{1}{2}=P(X=even)$$

Then

$$E(X)=0(\dfrac{1}{2})+50(\dfrac{1}{2})=25$$

 Daniel’s expected gain is ₱25.