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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?

Two-Events Conditionals


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?

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

Xander flips a coin and tosses a 6-sided dice. What is the probability that either the coin lands on Heads, or the dice lands on 4?

100 high school students are asked if they speak French. 70% of male students answer that they do not speak French, while 40% of female students answer they speak French. It is known that 40% of the responding students are female. If a randomly chosen student answers that he/she speaks French, what is the probability that this student is a female?

In a school, \( 30\% \) of the students are female, and \( 50\% \) of the students walk to school. If \( 20\% \) of the students are female and walk to school, what is the probability that a randomly chosen student is either female or walks to school?

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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