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. Using the Binomial distribution, what is the exact probability that more than 7 out of 10 these plants have red blossoms

Answer 1

The answer is "0.250".

Explanation:

Given:

`P(X=7) \\\\ n=10\\\\ p=0.75\\\\x \sim Binomial (n = 10, p = 0.75)\\`

`P(X=7) =\binom{n}{x} P^(x) (1-p)^((n-x)) \\\\`

`= \binom{10}{7}(0.75)^7(1-0.75)^(10-7) \\\\=120 * (0.75)^7 * (0.25)^3\\\\=0.250`