1. A card is drawn at random from a deck of playing cards. If it is red, the player wins 1 dollar; if it is black, the player loses 2 dollars. Find the expected value of the game.

Answer:

Total cards in deck = 52 Total red cards = 26 Total black cards = 26

The expected value = 1 * (26/52) - 2 * (26/52)

# to find the expected value
total_cards <- 52
total_red <- 26
total_black <- 26

# if red we win $1 and if lose we loose $2

expected_value <- 1 * (total_red/total_cards) - 2 * (total_black/total_cards)
expected_value
## [1] -0.5

So, the chances of loosing is high. It’s -0.5