Pierce

1.  Finding the Key.

Suppose you have 8 keys on your key ring.  One opens the front door to your house, and one opens the back door.  The other 6 will not help you get into your house.  You come home after dark, and randomly select a key.

a.  What are the odds that the key opens your front door?

b.  What are the odds against the key opening the back door?

c.  What are the odds in favor of the key opening a door of your house?

d.  You can rule out  one key because it is much too small to be a house key, and you can tell that by touching it.  Now answer questions a, b, and c  again.  Did the removal of one key change the odds considerably/

2.  Straight or Curly Hair?

Two parents with wavy hair can produce a child with hair that is straight, wavy, or curly.  Genetic theory states that the odds in favor of such a child having straight hair are 1:3, the odds in favor of wavy hair are 1:1, and the odds in favor of curly hair are 1:3.

Suppose two parents with wavy hair have one child.  What is the probability that the child has:

a.  straight hair?

b.  wavy hair?

c.  hair that is not curly?

Suppose two parents with wavy hair have two children.  What is the probability that:

d.  both have straight hair.

e.  at least one has straight hair?

Suppose your school contains 100 students whose parents both have wavy hair.  How many of those students would you expect to have curly hair?