Probability, Venn Diagrams, and Expected Values Training Spring 2019
Dive into the world of probability, Venn diagrams, and expected values with real-world scenarios involving dogs in a kennel, veterinary study data analysis, conditional probabilities, distribution tables, and more. Explore the concepts, calculations, and applications in a visual and engaging manner through various examples and illustrations.
Probability, Venn Diagrams, and Expected Values Training Spring 2019
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PROBABILITY, VENN DIAGRAM, AND EXPECTED VALUE TUTOR TRAINING SPRING 2019
WHICH DOGS GO WHERE? (VENN DIAGRAM) Twenty-four dogs are in a kennel. Twelve of the dogs are black, six of the dogs have short tails, and fifteen of the dogs have long hair. There is only one dog that is black with a short tail and long hair. Two of the dogs are black with short tails and do not have long hair. Three of the dogs have short tails and long hair. If all of the dogs in the kennel have at least one of the mentioned characteristics, how many dogs are black with long hair but do not have short tails?
PROBABILITY P(dog has a short tail) P(dog is black and has long hair) P(dog has a short tail but is not black)
WHICH DOG HAS WHAT? (TABLE FORMAT) In a study of 150 dogs seen by a veterinarian, researchers found the following: 35 dogs were obese; 42 have some sort of allergy; and 12 are obese and have some sort of allergy. Dog was normal weight Dog was obese Dogs had some sort of allergy? Total Yes No Total
CONDITIONAL PROBABILITY P(A dog did not have an allergy) Conditional probability shrinks the out of (population) which increases the probability The chance that I have high cholesterol increases because my dad has it. My out of is now my dad s side of the family and not the entire Mexican-American population. P(A dog had an allergy given that the dog was a normal weight) P(A dog was normal weight given the dog had an allergy)
PROBABILITY DISTRIBUTION (M&M S) A distribution table shows all the possible outcomes of an event. They are used to create Histograms in the Stats chapter and Probabilities in this chapter. When creating a probability distribution, start with creating a tree diagram. This utilizes the ideas of AND and OR probabilities. AND probabilities are multiplication problems OR probabilities are addition problems
PROBABILITY DISTRIBUTION Distribution for 2 red balls drawn out of a sack that contains, 2 green, 4 red, and 3 blue colored ping pong balls. P(2R) 4/9 * 3/8 12/72 P(1R) 2/9*4/8 + 4/9*2/8 + 4/9*3/8 + 3/9*4/8 40/72 P(0R) 2/9*1/8 + 2/9*3/8 + 3/9*2/8 + 3/9*2/8 20/72
PROBABILITY DISTRIBUTION (M&M S) First we separate and count up the M&M s Using only the Brown, Green, Orange, and Blue M&M s create a tree diagram that represents drawing out two M&M s With replacement vs Without replacement (AND Probabilities) Mutually Exclusive vs Overlapping (OR Probabilities) From the Tree Diagram the Distribution table can be constructed. 2 Brown or 2 Green or 2 Orange or 2 Blue
EXPECTED VALUE The amount of money that a person or entity expects to gain or lose over a long period of time playing the same game. Expected value uses both probability and odds in the calculation. Odds means money and can be manipulated; However odds, by definition, is the ratio of the probability of an event occurring vs the probability the event does not occur. Calculate the odds of rolling the sum of 11 on a pair of dice. The casinos give a player 15 to 1 odd in the game of Craps for rolling the sum of 11
CALCULATION OF EXPECTED VALUE The expected value of a medical insurance company insuring 35 people paying $15 bi-weekly The expected value of rolling the sum of 11 in the game of Craps If about 1 in 5 employees files a $500 claim each year, and If about 1 in 25 employees files a $2500 claim, and Multiply the probability by the money (odds) you expect to win and expect to lose Sum up the answers If about 1 in 32 employees files a $5000 claim
MEANING OF EXPECTED VALUE ANSWER In Craps, the Expected Value is -$0.11 which means; Over a long period of time playing, a player expects to lose 11 cents each game How much does the casino expect to win each game over the same period of time? Explain the meaning of the expected value for the insurance company.
LOTTERY TICKETS HYPE Is the probability affected by purchasing more than one lottery ticket? Are the odds affected by the purchasing of more than one lottery ticket? Does the expected value change when more than one lottery ticket is purchased?
