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# Conditional Probability

Conditional probability is the art of updating probabilities based on given information. What is the probability that the sidewalk is wet? And what if we know that it rained a few hours ago?

A survey on the preference for great composers in the 20\(^\text{th}\) century was conducted to 100 music critics. A part of the result is shown in the table below. What is the probability that a randomly chosen critic likes Stravinsky?

\[ \begin{array}{lcc} & \text{like Schoenberg} & \text{hate Schoenberg} \\ \text{like Stravinsky} & 40 & 25 \\ \text{hate Stravinsky} & 20 & 15 \end{array} \]

A card is drawn randomly from a standard deck of cards. What is the probability that the card drawn is either a 2 or a Spade?

**Details and Assumptions:**

A standard deck of cards consists of 52 cards, formed by 13 ranks (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen and King) of 4 suits (clubs, diamonds, hearts and spades).

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