Figuring Out Problems. MONTY HALL Problem MONTY HALL PROBLEM Stay or Switch Stay or Switch.

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Presentation transcript:

Figuring Out Problems

MONTY HALL Problem MONTY HALL PROBLEM Stay or Switch Stay or Switch

MONTY HALL Problem Using Inductive Reasoning

Inductive Conclusion: Bottom Up Example to Rule

Examples Inductive Reasoning I always hang pictures on nails. All pictures hang from nails. Many speeding tickets are given to teenagers. All teenagers drive fast Specific leans to General (ALL) Cell phone users around me talk too loud All cell phone users talk too loud

MONTY HALL PROBLEM Using Deductive Reasoning Using

Probability Rules of Chance Rules are general

Probability Chances I win 1/3 Chances I lose 2/3 STAY with one out of three or SWITCH to two out of three?

Deductive Conclusion: Rule to Example Top Down

10 Inductive vs. Deductive Historic

11 The notion of deductive reasoning - that is, to start with a premise and to then discard evidence that doesn't support the premise. "I think, therefore I am" Rule over observation

12 Galileo had used experiments as a research tool. Observation to Rule Inductive Reasoning Heliocentric Observation from telescope

13 Inductive Reasoning “All truths are easy to understand once they are discovered; the point is to discover them.” Galileo

Pattern to Rule 20, 30, 40, 50 X + 10 Inductive Reasoning

Pattern to Rule 20, 30, 40, 50 X , 4, 9, 16 X2X2 Inductive Reasoning

Pattern to Rule 20, 30, 40, 50 X , 4, 9, 16 X 2 4>2, 9>3, 16>4 X 2 > X Inductive Reasoning

Pattern to Rule 4>2, 9>3, 16>4 X 2 > X 0>0 or 1>1 Inductive Reasoning COUNTER EXAMPLE! Hidden Traps

Mary dropped her last five boyfriends! Jim is Mary’s boyfriend Deductive Reasoning, Inductive Reasoning, or neither? Is this a rule? Mary dropped her last five boyfriends! Jim will be dropped by Mary

R movies requires if under 17 a parent/adult guardian 21 to accompany. Deductive Reasoning, Inductive Reasoning, or neither? Carrie is 16 years old. Carrie needs parent/guardian for the R movie. Is this a rule? R movies requires if under 17 a parent/adult guardian 21 to accompany.

Deductive Reasoning, Inductive Reasoning, or neither? Is there a rule? Is it coming from examples?