Statistics for laboratory scientists

Homework problems for lecture 5

1. The seed of Mendel's pea plants were either smooth or wrinkled, the result of a single gene with two alleles, A (smooth) and a (wrinkled), with A dominant to a, so that seed with genotype AA or Aa are smooth and seed with genotype aa are wrinkled.

   We cross two pure-breeding lines, one with smooth seed and genotype AA and the other with wrinkled seed and genotype aa, to obtain the F₁ with genotype Aa

   We self an F₁ and pick a random F₂ seed.

   We grow up the F₂ and self it to obtain a random F₃ seed.

   Calculate the following.

   1. Pr(F₂ seed is smooth)

   2. Pr(F₂ seed has genotype Aa)

   3. Pr(F₂ seed has genotype Aa | it is smooth)

   4. Pr(F₃ seed is smooth | F₂ has genotype AA)

   5. Pr(F₃ seed is smooth | F₂ has genotype Aa)

   6. Pr(F₃ seed is smooth)

   7. Pr(F₃ seed is smooth | F₂ is smooth)

2. Consider the case of two urns. Urn A has 5 red balls and 5 blue balls. Urn B has 10 red balls. I flip a fair coin. If the coin lands heads, I make 2 draws with replacement from urn A. If the coin lands tails, I make 2 draws with replacement from urn B.

   Calculate the following.

   1. Pr(balls are both red | coin was heads)

   2. Pr(balls are both red | coin was tails)

   3. Pr(2nd ball is red | 1st ball is blue)

   4. Pr(2nd ball is red | 1st ball is red)

3. Consider drawing 3 cards (without replacement) from a well-shuffled deck.

   Calculate the following.

   1. Pr(3rd card is a Jack)

   2. Pr(3rd card is a Jack | 1st card is a heart)

   3. Pr(3rd card is a Jack | 1st two cards are Jacks)

   4. Pr(All of the cards are Jacks)

   5. Pr(None of the cards are Jacks)

   6. Pr(At least one of the cards is a Jack)