Question

According to genetic theory, the blossom color in the second generation of a certain cross of sweet peas should be red or white in a 3:1 ratio. That is, each plant has probability 3/4 of having red blossoms, and the blossom colors of separate plants are independent.

a. What is the probability that exactly three out of four of these plants have red blossoms?

b. What is the mean number of red-blossomed plants when 60 plants of this type are grown from seeds?

c. What is the probability of obtaining at least 45 red-blossomed plants when 60 plants are grown from seeds? Use the Normal approximation. If your software allows, find the exact binomial probability and compare the two results.

Answer 1

Given that

The blossom color of red or white in the ratio = 3:1

Each plant has probability of having red blossoms = 3/4 = 0.75

a)

The probability that exactly 3 out of 4 of these plants have red blossoms

By using binomial distribution,

= 0.4219

b)

Mean = np = 60 * 0.75 = 45

c)

The probability of obtaining at least 45 red-blossomed plants when 60 plants are grown from seeds

= 0.5688