In: Statistics and Probability
Genetics: According to genetic theory, the blossom color in the second generation of a certain cross of sweet peas should be red or white. Each plant has a probability of 3/4 of having red blossoms, and the blossom colors of separate plants are independent. You are testing 10 pea plants for their blossoming behavior.
a. Explain why the event “having red blossom” in this specific context is binomial using the four characteristics of a binomial setting.
b. What is the probability that all 10 pea plants do not have red blossoms?
c. What is the probability that at least one of the ten pea plants has red blossoms? (Hint: Use part c) to answer this question)
d. Based on the probability that you computed in part c), would you question the true probability of pea plants developing a red blossom? Explain your answer.