3.01 You have a bag filled with 20 red marbles and 20 blue marbles. You shake the bag so that the marbles are thoroughly mixed.

(a) You reach in the bag without looking, and draw out one marble. What is the probability that it is red?

(b) What is the probability of drawing out two blue marbles in a row, assuming that you replace the first marble and remix the bag before drawing the second?

(c) The answer to part (b) would be different if you did not replace the first marble. Why is this true? Consider how the the probability for the second marble changes depending on the color of the first marble drawn from the bag.

(d) Given your answer to part (c), why can't you use the product rule to calculate the probability of drawing two blue marbles in a row, if the first one is not replaced?

3.02 You are rolling a standard die. Calculate the probability of each of the following events.

(a) Rolling a 4.

(b) Rolling a 5 or a 6.

(c) Rolling a 3 or an odd number.

(d) Which probability rule can you use to calculate the answer to part (b), and why can you not use the same rule to calculate the answer to part (c)?

3.03 On the average, about one child in every 10,000 births in the U.S. has a genetic disease called phenylketonuria (PKU).

(a) What is the probability that the next child born in a particular Mississippi hospital will have PKU? You can assume that the probability of the disease in Mississippi is the same as in the US.

(b) Suppose a PKU child has just been born in this hospital. What is the probability that the next child born in the same hospital will have PKU?

(c) What is the probability that two children born in a row will have PKU?

(d) Question (b) and (c) seem the same, but they are not. Why is the answer to part (c) so different from the answer to part (b)?

3.04 In peas, axillary flowers (A) is dominant to terminal flowers (a), and colored flowers (R) is dominant to white (r). A true-breeding plant with white, terminal flowers is crossed with a true-breeding plant having colored, axillary flowers. The F₁ plants are then allowed to self-pollinate.

(a) Use the forked-line method to calculate the probability of each possible F₂ genotype.

(b) Use the forked-line method to calculate the probability of each possible F₂ phenotype.

3.05 In peas, Green pods (G) is dominant over yellow pods (g), and inflated pods (I) is dominant over constricted pods (i). The following cross is made: Gg Ii x Gg ii. Without constructing a Punnett square, calculate the probability of each of the following.

(a) What is the probability that an offspring will be homozygous dominant for the pod color gene?

(b) What is the probability that an offspring will be homozygous dominant for the pod shape gene?

(c) What is the probability that an offspring will have green inflated pods or yellow constricted pods?

(d) What proportion of the progeny would you expect to be heterozygous for both genes?

3.06 In a certain trihybrid cross, both parents have genotype Aa Bb Cc. Calculate the following without constructing a Punnett square or drawing a forked-line diagram:

(a) What is the probability that this cross will produce an offspring that is shows the recessive phenotype for all three traits?

(b) What is the probability of producing an offspring with the phenotype A- bb C-? (The notation "A-" means that the offspring has the dominant phenotype but might be either homozygous or heterozygous. That is, it has at least one dominant allele.)

(c) If you had worked these problems using a Punnett square, how many boxes would it have to contain?

3.07 Three traits in cats are being studied. Long hair (L) is dominant over short (l). White-spotted (S) is dominant over solid colored(s), and dilute color (D) is dominant over non-dilute (d). Two cats with genotypes ll Ss dd and Ll Ss Dd are crossed. Calculate each the following without constructing a Punnett square or drawing a forked-line diagram:

(a) What is the probability of this cross producing an offspring with genotype ll ss dd?

(b) What is the probability of this cross producing an offspring with the phenotype of short-hair, white-spotted, non-dilute?

3.08 Two pure-breeding rats with contrasting phenotypes for two different traits were crossed, AA bb x aa BB, then the F₁ rats were crossed among themselves. In the F₂ progeny, 50 rats displayed both dominant phenotypes (A- B-). Of these 50 rats, how many you predict to have the double heterozygous genotype (Aa Ba)?

3.09 Assuming that the probability of having a girl on any given birth is 0.5, consider calculating the probability that a family of four will consist of three girls and one boy.

(a) First, calculate the answer to this question by writing out all possible birth orders and determining what fraction of the families fit the required family makeup.

(b) Now calculate the answer again using the binomial formula.

(c) It turns out that the true probability of having a boy or girl on any one birth at not quite equal. The actual proportion of girls at birth is about 0.49, rather than 0.50. Given this more accurate value, recalculate the probability of having a family of three girls and one boy?

(d) Could you calculate the answer to (c) by counting birth orders as you did in part (a)? Why or why not?

3.10 Assuming the probability of having a boy is equal to the probability of having a girl, what is the probability that a family with 5 children will consist of:

(a) 3 daughters and 2 sons?

(b) alternating sexes?

(c) alternating sexes, starting with a son?

(d) all daughters?

(e) all the same sex?

(f) at least 4 daughters?

(g) a daughter as the eldest child and a son as the youngest?

3.11 In Drosophila, vestigial (crinkled) wings is recessive to normal wings ("wild type"). A true-breeding wild type female is crossed with a vestigial male. Two F₁ flies are then crossed to obtain the F₂ generation. If the F₂ generation has 8 flies, what is the probability of that 5 will be wild type and 3 will be vestigial?