Exercise 1
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?
|S| = \(\binom{9}{1}\), All possible combo in the sample space
|even| = \(\binom{5}{1}\), Even sample space and its combo
|odd| = \(\binom{4}{1}\), Odd sample space and its combo
#Probability of wininng => is drawing even. There are 5 even numbers
# using combinations
peven <- choose(5,1)*choose(4,0)/choose(9,1)
round(peven ,4)## [1] 0.5556#Probability of losing => is drawing odd. There are the left over odd numbers
podd <- 1- peven
round(podd,4)## [1] 0.4444# The expected value proposition
E <- 1*peven - 1*podd
round(E,4)## [1] 0.1111