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M119L09to10-page7

# M119L09to10-page7 - 255 245 be a probability anyway Note If...

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(Lesson 9: Probability Basics; 4-2) 4.07 Approach 2): Frequentist / Empirical Approach Let N = total # of trials observed. If N is “large,” then: P A ( ) # of trials in which A occurred N Example 5 A magician’s coin comes up heads (H) 255 times and tails (T) 245 times. Estimate P H ( ) for the coin, where P H ( ) = P coin comes up "heads" when flipped once ( ) . Solution to Example 5 First, N = 255 + 245 = 500 . P H ( ) 255 500 = 0.51 Warning: Divide 255 by 500, not by 245. Why can’t
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Unformatted text preview: 255 245 be a probability, anyway? Note: If the coin is, in fact, fair, then our estimate for P H ( ) will approach 1 2 , or 0.5, if we flip the coin more and more times; i.e., as N gets larger and approaches infinity. In symbols: P H ( ) → 1 2 as N →∞ . This is a consequence of the Law of Large Numbers (LLN)....
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