Time for MATH MINUTE! (provide your favorite theme music here). 

         Get out your paper & pencil, because I have a new puzzle for you!!

PUZZLE #104 Sets, sets, and more sets.

 

A. Recall that two sets can have nonempty intersections, and three sets can have nonempty intersections between any two sets or all three sets.

 

       Suppose you have a group of 30 students which have the following characteristics:

       10 have brown hair,

       18 wear jeans,

       16 wear glasses.

Also, 9 wear jeans and have glasses,

        7 have brown hair and wear jeans,

        5 have brown hair and glasses,

        3 have brown hair, wear jeans, and wear glasses

 

       Can you determine how many have brown hair but do not wear jeans?

       How about how many wear jeans and do not wear glasses?

       Do all of the students have brown hair, or wear jeans, or wear glasses?

       If not how many do you find?

 

B.  First recall some results from probability theory.

       If you have say 3 flowers, one red, one pink, and one yellow, then the probability that someone will pick a red colored flower without prejudice (blindfolded) is 1/3.

       If someone blindly picks one of the 3 flowers and then picks another, with the desire of getting a red one and a pink one, look at all of the possible outcomes, two of them will have a red and a pink flower, and four of them will have a yellow flower, so the probability is 2/6 = 1/3.

       OK, now suppose you are getting a yogurt out of the refrigerator, and you have 3 blueberry, 2 peach, and 1 strawberry yogurts in it.

       What is the probability of getting a peach yogurt, assuming you can not see the labels when you choose?

       Suppose you pick a yogurt and it is not peach, so you put it back and choose another one, now what is the probability of getting a peach yogurt?

       What if you want a peach and a strawberry yogurt?

 

Have fun!

 

         Send your comments, ideas and solutions before Monday to the email below, and in the subject line be sure to put  MM  in the subject line

                                     parksjm@potsdam.edu

         Visit us here online at:

                           http://www2.potsdam.edu/parksjm/MM1.1.htm 

to see the results every Friday.

         See you next time on MATH MINUTE!  (theme music fades out here).