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CONDITIONAL PROBABILITY

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Conditional Probability Knowledge that one event has occurred changes the likelihood that another event will occur. Denoted: P(A|B) The probability of A given than B has already occurred.

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Ex: Population has.1% of all individuals having a certain disease. A test is available and 80% of those who test positive actually have the disease. E = the individual has the disease F = the individual’s diagnostic test is positive P(E) = P(E | F) = Before the test, the occurrence of E was highly unlikely, after the test turns out positive it’s highly likely.

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Example: Titanic 1st Class 2nd Class 3rd Class Survived Died P(3 rd class)P(3 rd class | survived) P(1 st class | survived)P(died | 2 nd class)

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Students at the University of New Harmony received 10,000 course grades last semester Find P(lower than B) Find P(E|Low) and P (Low|E). Which of the above tells you whether this college’s engineering students tend to earn lower grades than students in liberal arts. Total Total

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Find the probability of drawing a 3 of diamonds if you already know that it’s a red card.

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Find probability of a family having 2 girls given that they have at least 1 girl.

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A consumer organization estimates that over a 1-year period 17% of cars will need to be repaired once, 7% will need repairs twice, and 4% will require 3 or more repairs. Probability that a car chosen at random will need a. No repairs b. No more than one repair c. Some repairs

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You randomly draw a card at random from a standard deck of 52 cards. P(heart | red) P(red | heart) P(ace | red) P(queen | face card)

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70% of kids who visit a doctor have a fever, and 30% of kids with a fever have sore throats. What’s the probability that a kid who goes to the doctor has a fever and a sore throat?

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In a class of 45 students 18 like apples and 32 like bananas and 5 dislike both fruits. If a students is randomly selected, find the probability that the student: likes both fruit Likes at least one fruit Likes Bananas given that they like apples Dislikes apples given that they like bananas.

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Independent Events

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Using the blocks: What’s the probability of drawing a green? If I replace the block and draw again what is the probability that the second block is green?

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Using the blocks: What’s the probability of drawing a green? If I do not replace the block and draw again what is the probability that the second block is green?

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So…. Sampling with replacement is ____________ Sampling without replacement is ________________

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If I roll 2 dice, what’s the probability that I get a three on both? Independent or Dependent?

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Is there a relationship between gender and handedness? To find out, we used CensusAtSchool’s Random Data Selector to choose a SRS of 50 Australian high school students who completed a survey. Dominant hand GenderRightLeftTotal Male20323 Female23427 Total43750

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If two events are not independent, does that mean than there actually is a relationship between the two variables? No…not necessarily

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Independent or not independent? Shuffle a standard deck of cards, and turn over the top card. Put it back in the deck, shuffle again, and turn over the top card. Define events A: first card is a heart B: second card is a heart

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Independent or not independent? Shuffle a standard deck of cards, and turn over the top two cards, one at a time. Define the events A: first card is a heart B: second card is a heart

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Independent or not independent? The 28 students in a class completed a brief survey. One of the questions asked whether each student was right- or left-handed. Choose a student from the class at random. The events of interest are “female” and “right-handed.” Gender HandednessFemaleMale Left31 Right186

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Multiplication Rule Dependent: Independent:

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P(King and then King) with replacement.

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P(king & King) without replacement.

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P(king and 4) without replacement

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P(E)=.2 P(F)=.3 Find P(E and F) if they are independent.

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If P(A) = 0.2 and P(B) =.4 and P(A B) = p. Find p if A and B are mutually exclusive A and B are independent

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Using a tree diagram, what’s the probability of getting two heads when you toss a fair coin?

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Suppose that 60% of all customers of a large insurance agency have automobile policies with the agency, 40% have homeowner’s policies, and 25% have both types of policies. If a customer is randomly selected, what is the probability that he or she has at least one of these two types of policies with the agency? (Look at Venn Diagram)

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The probability of purchasing a Soni DVD player is The probability of an extended warranty being purchased when a Soni DVD player is bought is Find the probability that a person buys a soni DVD and the extended warrranty.

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Homework Page 329 (63, 65, 67, 69, 71, 73, 75, 79, 106)

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