Question

You are studying a variety of pea plant that has either red flowers or white flowers. When you cross true-breeding red-flowering plants with true-breeding white-flowering plants, you get all red-flowering plants in the F1 generation. If you then allow the F1 plants to self-fertilize, you observe that 75% of the F2 plants are red-flowering plants, while 25% of the F2 plants are white-flowering plants. Next you make 640 different monohybrid crosses and decide to analyze only the first 8 plants produced from each of these crosses (i.e. a total of 5120 progeny plants total). How many of these crosses would be expected to produce 6 red plants and 2 white plants?

Answer 1

approximately 200

Step-by-step explanation:

From the question, we have

probability of red = 0.75

Probability of white = 0.25

We are required to find the probability of 6 red + 2 white plants offspring and after we do we multiply it by 640

We will solve this using the binomial theorem method

(a+b)⁸ = a⁸+8a⁷b+28a⁶b²+56a⁵b³+70a⁴b⁴+56a³b⁵+28a²b⁶+8a¹b⁷+b⁸

The required probability is 28a⁶b²

a = 0.75

b = 0.25

= 28 x 0.75⁶ x 0.25² x 640

= 28 x 0.178 x 0.0625 x 640

= 199.36

Which is approximately 200 crosses would be needed