A very large gardening business grows rose bushes for sale to garden stores around the world. The most popular colors are red, pink, and white. The business decides on 50% red roses, 30% pink, and 20% white. A gardener orders 10 rose bushes selected randomly from a huge field. Her primary interest is in pink roses. Assuming rose bushes are selected independently, the number of pink rose bushes can be modeled by a binomial distribution. The probability of getting 1 pink rose bush is:

Question

Quizplus · Accepted Answer

Since the gardener's primary interest is pink roses, we only care about the probability of selecting a pink rose out of the 10 bushes. We know that the overall percentage of pink roses in the huge field is 30%. Therefore, the probability of selecting a pink rose on any particular selection is 0.3. Since we are selecting 10 bushes independently, we can use the binomial distribution to calculate the probability of getting exactly 1 pink rose as:
P(X = 1) = (10 choose 1) * 0.3^1 * 0.7^9 ≈ 0.39
Therefore, the probability of getting 1 pink rose bush is about 0.39, which corresponds to choice C.

A Very Large Gardening Business Grows Rose Bushes for Sale