The following problems are to help you sharpen and deepen your understanding of simple probabilities and simple Mendelian ratios. Problems are not to be handed in and will not be graded. We will discuss the problems in recitation on Friday, Sept. 5.

1. You have three dice-- black, white and yellow. You roll all three dice at the same time. Calculate the probabilities of the following outcomes:

• Rolling three sixes
  
• Rolling sixes on the black and yellow dice, and a 5 on the white die.
  
• Rolling no sixes at all
  
• Rolling two sixes and one five (on any color die)
  
• Rolling the same number (any number) on all three dice

2. Two black guinea pigs were mated repeatedly over several years. They produced 29 black progeny and 9 white progeny. Explain these results, giving the genotypes of parents and progeny.

3. (a) Maria has two children. One of them is a girl. What is the probability that the other one is also a girl?
    (b) Carlotta has one daughter and is now pregnant. What is the probability that her next child will be a girl?
    (c) Is there any difference between the problems in (a) and (b)? If so, what is it?

4. You will get $100 if you pick a red ball from one of two opaque jars. One jar contains 50 red and 50 black balls. The other contains 90 balls of one color and 10 balls of the other color. You get only one pick. Which jar would you pick from, and why? (Note: This is a quantitative question, not a blind guess.)

5. In the fruitfly Drosophila melanogaster, wild-type (gray) body color is caused by a dominant gene e⁺ and "ebony" body color by the recessive allele e. Normal wing size is produced by the dominant allele vg⁺ and vestigial (nearly absent) wings by the recessive allele vg. Work out the expected phenotypic ratios for the following cross:

vg+vg e+e  X vg+vg ee