A card is drawn randomly from a standard deck of cards. you win $10 if the card is a spade or an ace. what is the probability that you will win the game?

The probability of winning is 4/13.

These two events are not mutually exclusive; this means they can happen at the same time. For two events that are not mutually exclusive,

P (A or B) = P (A) + P (B) - P (A and B)

This gives us

P (spades or Ace) = P (spades) + P (Ace) - P (spades and Ace)

There are 13 spades out of 52 cards.

There are 4 aces out of 52 cards.

There is 1 card that is a spade and an ace out of 52 cards.

13/52 + 4/52 - 1/52 = 16/52 = 4/13