Question

Blue moon beans produce beans that are either the dominant color blue or the recessive color white The bean pods for this species always contain four seeds each. Two heterozygous plants that each have the Bb genotype are crossed.
Part A
What is the predicted frequency if there are four blue beans in pod? Express your answer to three decimal places.
Part B
What is the predicted frequency if there are three blue and one white bean in pod? Express your answer to three decimal places.
Part C
What is the predicted frequency if there are two blue and two white beans in pod? Express your answer to three decimal places
Part D
What is the predicted frequency if there are one blue and three white beans in pod? Express your answer to three decimal places.
Part E
What is the predicted frequency if there are four white beans in pod? Express your answer to three decimal places.

Answer 1

Answer:

a) $0.316$

b) $0.105$

c) $0.035$

d) $0.0117$

e) $0.0039$

Explanation:

When two heterozygous plants with genotype Bb are crossed, following offspring are produced

Bb * Bb

BB, Bb, Bb, bb

so the probability of blue offspring is $\frac{3}{4}$ and the probability of white offspring is $\frac{1}{4}$

a) Probability of all 4 peas as blue

$\frac{3}{4} * \frac{3}{4} * \frac{3}{4} * \frac{3}{4} \\= \frac{81}{256} \\= 0.316$

b) Probability of 3 blue and 1 white

$\frac{3}{4} * \frac{3}{4}* \frac{3}{4}* \frac{1}{4}\\= \frac{27}{256} \\= 0.105$

c) Probability of 2 blue and 2 white

$\frac{3}{4} * \frac{3}{4}* \frac{1}{4}*\frac{1}{4}\\= 0.035$

d) Probability of 1 blue and 3 white

$\frac{3}{4} * \frac{1}{4} * \frac{1}{4}* \frac{1}{4}\\= \frac{3}{256} \\= 0.0117$

e) Probability of all white

$\frac{1}{4} * \frac{1}{4} * \frac{1}{4} * \frac{1}{4} \\= \frac{1}{256} \\= 0.0039$