ࡱ> UWTi \bjbjO O 4-a-a.BBBBBVVVV\\VvULZZZZo!o!o!TTTTTTT$XD[ZTiBo! o!o!o!TBBZZ] 0US#S#S#o!RBZBZTS#o!TS#S#%QDATZ`2!iR&TFU0vUR\O"\LAT\BATLo!o!S#o!o!o!o!o!TT #Fo!o!o!vUo!o!o!o!\o!o!o!o!o!o!o!o!o! :  STAR SIGNS Five people meet at a party. What is the chance that at least two of them have the same star sign? Place your estimate on this line.  No chance 50/50 chance Almost certain STAR SIGNS Five people meet at a party. What is the chance that at least two of them have the same star sign? Place your estimate on this line.  No chance 50/50 chance Almost certain STAR SIGNS Five people meet at a party. What is the chance that at least two of them have the same star sign? Place your estimate on this line.  No chance 50/50 chance Almost certain STAR SIGNS Five people meet at a party. What is the chance that at least two of them have the same star sign? Place your estimate on this line.  No chance 50/50 chance Almost certain STAR SIGNS Five people meet at a party. What is the chance that at least two of them have the same star sign? Place your estimate on this line.  No chance 50/50 chance Almost certain eidfghacb^_( Do you think the chance of two or more in a group of five having the same star sign is: High (more than 75%) About 75% More than 50%, but less than 75% About 50% Less than 50%, but more than 25% About 25% Low (less than 25%) Check with the group you are in. Are there two of you with the same star sign? eidfghacb^_( eidfghacb^_( Discuss in your group how to do an experiment to estimate this probability. How could we design a model to simulate this problem? What simplifying assumptions would we have to make? What is a trial? What is a success? eidfghacb^_( Carry out a series of trials. Record in a table. TrialOutcomeSuccessFailure123 etc nTotal  eidfghacb^_( eidfghacb^_( Record your group s results in table below. GroupNumber of SuccessesTotal number of trials eidfghacb^_( eidfghacb^_( Challenge: Can you work out the theoretical probability of success? How accurate was your experiment? eidfghacb^_( Hints. Start with the simple problem (group of 2) and build up. First investigate the probability that no  matches will occur in groups of 2, 3, 4 and 5. Once probability of no  matches is found, find probability of a match. eidfghacb^_( eidfghacb^_( Probability of no match in a group of 2 is  EMBED Equation.3 . Probability of no match in a group of 3 is  EMBED Equation.3 . Probability of no match in a group of 4 is  EMBED Equation.3 . Probability of no match in a group of 5 is  EMBED Equation.3 = 0.38. Therefore the probability of a match occurring in a group of 5 is 1-0.38 = 0.62. How does this match up with the experimental results? eidfghacb^_( eidfghacb^_( eidfghacb^_( eidfghacb^_( eidfghacb^_(eidfghacb^_( Star signs activity. See also Birth Month Paradox and Star Signs sheet. 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There are also some sheets with the twelve signs on for groups who want to use this method. Packs of cards are also needed. **Check to see if we have 12 sided dice. Two lessons have been allowed for this activity. Lesson One: Should get to the point where the individual group results are recorded on the overhead. Calculate the class probability of success. Discuss in your group how to do an experiment to estimate this probability. How could we design a model to simulate this problem? Use packs of cards with 12 cards to represent the 12 star signs. Put the 12 star signs in a hat/box. Use a 12 sided dice. What simplifying assumptions would we have to make? That all star signs are equally likely to occur. What is a trial? Turn over 5 cards from 5 different decks or draw 5 cards from one deck, returning the selected card in between each draw and shuffling the deck. Draw 5 star signs from the hat, returning the selected one in between each draw. 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