Question

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?

Answer 1

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